CD 

r- 
o 


MECHANICS'  TABLES, 

CONTAINING 

AREAS  AND   CIRCUMFERENCES   OF  CIRCLES, 

AND    SIDES  OF  EQUAL  SQUARES  ; 

CIRCUMFERENCES  OF  ANGLED  HOOPS, 

ANGLED  OUTSIDE  AND  INSIDE; 

CUTTING   OF   BOILER  PLATES, 
COVERING    OF   SOLIDS,   &c., 

•  AND  WEIGHTS  OF  VARIOUS  METALS, 

&c.,  &c.,  &c.,  &c. 

MISCELLANEOUS    NOTES, 

COMmiSING 
DIMENSIONS    OF   MATERIALS,  ALLOYS,  PAINTS,  LACKERS,  &C. 


BY  CHARLES  H.  HASWELL, 

MARINE  ENGINEER, 


NEW  YORK: 
HARPER  &  BROTHERS,  PUBLISHERS, 

FRANKLIN    SQUARE. 

1856. 


v*V 


Entered,  according  to  Act  of  Congress,  in  the  year  one  thousand 
eight  hundred  and  fifty-six,  by 

HARPER  <fc  BROTHERS, 

in  the  Clerk's  Office  of  the  District  Court  of  the  Southern  District 
of  New  York. 


TO 

THE  MECHANICS 

OF   THE 

UNITED  STATES  OF  AMERICA, 

IN  the  compilation  and  construction  of  the  following 
tables  and  rules,  my  purpose  has  been  that  of  furnishing 
for  jour  ready  reference  such  calculations  and  instructions 
as  were  best  suited  for  the  greatest  number  of  you,  and,  at 
the  same  time,  to  limit  the  extent  of  the  work  within  the 
requirements  of  convenience  of  reference  and  economy  of 
cost. 

My  attention  was  first  called  to  the  demand  for  a  work 
of  this  character  by  James  Murphy,  Esq.,  a  proprietor  of 
the  Fulton  Iron  Works  of  this  city,  and  I  avail  myself  of 
this  opportunity  to  express  my  thanks  to  him  for  his  valu- 
able suggestion- 

CHAS.  H.  HASWELL, 

6  Bowling  Green,  N.  Y. 
April  Uth,  1856. 


262652 


CONTEXTS, 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES,  in  Inches  and  Eighths 5 

ABEAS  AND  CIECUMFEEENCES  OF  CHICLES  AND  SIDES  OF  EQUAL  SQUARES,  ad 

vanning  ly  an  Inch  or  twelfth  of  an  Inch 10 

CIBCUMFEEENCES  OF  CIRCLES,  in  Feet,  Inches,  and  Eightlis 16 

Appli  ation  of  the  Table  of  Areas  and  Circumferences  to  the  construction 

of  teetlied  Wheels 26 

CIRCUMFERENCES  OF  ANGLED  HOOPS  (angled  outside) 27 

(angled  inside) 32 

CUTTING  OF  BOILEK  PLATES,  MATERIALS  FOP.  ROOFING,  AND  THE  COVERING 

OF  SOLIDS 37 

Application  of  the  Rules  to  the  Shells  of  cylindrical  Betters  and  Flues 44 

WROUGHT  IRON 

Weight  of  Square  Rolled  Iron 48 

Weight  of  Round  Rolled  Iron  Shafting 49 

Weight  of  Flat  Rolled  Iron 51 

Application  of  the  Tables 54 

OA&T  IRON 56 

To  find  the  Weight  of  a  Piece  of  Cast  or  Wrought  Iron 55 

LEAD 5ft 

WEIGHT  OF  COPPER  RODS  OR  BOLTS 57 

COPPEE 57 

Brazier's  Sheets  and  Sheathing  Copper ' 57 

WEIGHT  OF  A  SQUARE  FOOT  OF  CAST  AND  WROUGHT  IEON,  COPPER,  AND 

LEAD 5$ 

WF.IGUT  OF  RIVETED  COPPER  PIPES 59 

BRASS 50 

WEIGHT  OF  CAST  IRON  PIPES 60 

WEIGHT  AND  CAPACITY  OF  CAST  IRON  AND  LEAD  BALLS 62 

WEIGHT  OF  LEAD  PIPE  PEE  YARD. .* 65 

WEIGHT  OF  A  SQUARE  FOOT  OF  WROUGHT  IRON,  as  per  wire  gauge 64 

Values  of  the  birmingham  Gauges 64 

LAP-WELDED  IRON  BOILER  TUBES 65 

SCREWS * 65 

£IN 65 

ALLOYS  OF  COPPER,  AND  TIN,  &c.  v 66 

SOLDEES ; 6T 

CEMENTS ;  i — - 67 

Hydraulic,  Cement •  •  •  •  67 

Brown  Mortar 67 

DIGGING 6T 

GAS  PIPES 68 

CISTERNS 6» 

WEIGHTS  OF  VARIOUS  SUBSTANCES 6D 

WEIGHT  OF  COMPOSITION  SHEATHING  NAILS • 69 

SLATING TO 

HEMPEN  CORDS TO 

STRENGTH  AND  STIFFNESS  OF  METALS To 

PAINTS  AND  LACKERS .• 71 

Staining  Wood  and  Ivory » , 72 


\ 


HASWELL'S  MECHANICS'  TABLES, 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES, 
From  -fall  to  100. 


Diam.         Area. 

]     Circum. 

Diam. 

Area. 

Circum. 

j  Diam.         Area. 

1    Circum. 

-Jj        .00019 

!      .0490 

4. 

12.566 

12.57 

10.         78.541 

31.42 

^3        .00076 

.0951 

i 

13.364 
14.186 

12.96 
13.35 

4      80.51a 
.*;     82.516 

1    31.81 
32.20 

£J     .00306 

.1963 

_i 

15.033 

13.74 

.f       84.54C 

!    32.59 

i          01227 

.3926 

Ji 

15.904 

14.14 

4       86.59C 

32.99 

B,   1 

jk 

16.800 

14.53 

4       88.664 

33.38 

iir  i     .02761 

.5890 

_Jl 

17.720 

14.92 

.f       90.762 

:    33.77 

i        .04908 

.7854 

4 

18.665 

15.32 

4      92.885 

!    34.16 

&        .07669 

.9817 

5. 

19.635 
20.629 

15.71 
16.10 

11.    ;     95.033 
4       97.205 

34.56 
34.95 

|        .1104 

1.178 

,1 

21.648 

16.49 

A       99.402 

35.34 

7         .1503 

1.374 

.s 

22.690 

16.89 

.|     101.62 

35.74 

•  y 

23.758 

17.28 

.1]  103.87 

36.13 

i-        .  1963 

1.571 

•1 

24.850 

17.67 

.$;  106.14 

36.52 

j9,.        .2485 

1.767 

.A 

25.967 

18.06 

.f     108.43 

36.91 

4 

^27.108 

18.46 

.f!  110.75 

37.31 

|        .3067 

1.963 

6.8 

28.274 

18.85 

12.       113.10 

37.70 

ai        .3712 

2.159 

4 

29.464 

19.24 

4     115.47 

38.09 

f        .4417 

2.356 

•| 

30.680 
31.919 

19.64 
20.03 

4i  117.86 
.|     120.28 

38.48 
38.88 

££        .5174 

2.551 

•  1 

33.183 

20.42 

4     122.72 

39.27 

f-        .6013 

2.749 

4 

34.471 

20.81 

.|     125.18 

39.66 

f  i 

35.785 

21.21 

.f     127.68 

40.06 

if       .  6902 

2.945 

•!• 

37.122 

21.60 

.1  1   130.19 

40.45 

1.          .7854 

3.142 

7  ^ 

38.484 

».99 

13.    !  132.73 

40.84 

1.9940 

3.534 

.1 

39.871 

.38 

4-j  135.30 

41.23 

1  .  227 

3.927 

.1 

41.282 

22.78 

4     137.89 

41.63 

1.485 

4.320 

4 

42.718 

23.17 

.|i  140.50 

42.02 

1.767 

4.712 

•» 

44.179 

23.56 

4     143.14 

42.41 

2.074 

5.105 

•f 

45.663 

23.95 

.|     145.80 

42.80 

..      2.405 

5.498 

A 

47.173 

24.35 

.f     148.49 

43.20 

.|      2.761 

5.891 

•I 

48.707 

24.74 

.|j  151.20 

43.59 

2.        3.142 

6.283 

8. 

50.265 

25.13 

14.       153.94 

43.98 

4     3.547 

6.676 

4 

51.848 

25.52 

1156.70 

44.38 

.-I-     3.976 

7.069 

1 

53.456 

25.92 

|  159.48 

44.77 

.1     4.430 

7.461 

•8 

55.088 

26.31 

162.29 

45.16 

.£     4.909 

7.854 

4JL 

56.745 

26.70 

165.13 

45.55 

.|     5.412 

8.247 

•f 

58.426 

2V.  10 

167.99 

45.95 

.£     5.940 

8.639 

.& 

60.132 

27.49 

170.87 

46.34 

.|     6.492 

9.032 

4 

61.862 

27.88 

173.78 

46.73 

3.        7.069 

9.425 

9'. 

63.617 

28.27 

15.       176.71 

47.12 

4     7.670 

9.818 

4 

65.396 

28.66 

41  179.67 

47.52 

•i     8.296 

10.210 

.1 

67.200 

29.06 

ij  182.65 

47.91 

.f     8.946 

10.602 

4 

69.029 

29.45 

.|    185.66 

48.30 

.*•      9.621 

10.995 

,i 

70.882 

29.85 

.|     188.69 

48.69 

4    10.321 

11.388 

•X 

72.759 

30.24 

4     191.75 

49.09 

4    11.045 
4  H1.793 

11.781 
12.173 

_£ 

•! 

74.662 
76.588 

30.63 
31.02 

.f  !  194.83 
4i  197.93 

49.48 
49.87 

AREAS    AND    CIRCUMFERENCES    OF    CIRCLES. 


TABLE — (Continued). 


Dlam. 

Area, 

Cireum. 

Diana,    Area,   •  Cireum. 

Dinm,  ;   Area,   .  Cireum. 

16. 

201.06 

50.27 

23. 

415.48 

72.26 

30.   706.86 

94.25 

204.22 

50.66 

.1 

420. 

72.65 

712.76 

94.64 

^  . 

207.39 

51.05 

.}|  424.56   73.04 

718.69 

95.03 

210.60 

51.44 

.1  429.13 

73.43 

, 

724.64 

95.43 

t.  . 

213.82 

51.84 

.1  433.74 

73.83 

730.62 

95.82 

J  , 

217.08 

52.23 

4'i  438.36 

74.22 

736.62 

•  96.21 

220.35 

52.62 

,|  443.01 

74.61 

742.64 

96.60 

223.65 

53.01 

.1  447.70 

75. 

. 

748.69 

97, 

17  ! 

226.98 

53.41 

24.  '452.39 

75.40 

81. 

754,77 

97.39 

•1 

230.33 

53.80 

.4  457.11 

75.79 

i 

760.87 

97.78 

_JL 

233.70 

54,19 

.}  461.86 

76.18 

1 

766.99 

98.17 

i 

237.10 

54.59 

.$  466.64 

76.58 

,ji  . 

773.14 

98.57 

•^ 

240.53 

54.98 

^  471.44 

76.97 

.j. 

779.31 

98,97 

•f 

243.98 

55.37 

•f 

476.26 

77.36 

j 

785.51 

99.35 

a 

247.45 

55.76 

.3. 

481.11 

77.75 

J 

791.73 

99.75 

'8 

250.95 

56.16 

.|  485.98 

78.15 

J 

797.98 

100.14 

18. 

254.47 

56.55 

25. 

490.87 

78.54 

32. 

804.25 

100.53 

i 

258.02 

*  56.94 

•i 

495.80 

78.93 

810.54 

100.92 

,i 

261.59 

57.33 

.1  500.74 

79.33 

816.86 

101.32 

•8 

265.18 

57.73 

.1  505.71 

79.72 

823.21 

101.71 

A 

268.80 

58.12 

.1]  510.71 

80.11 

829.58 

102.10 

I 

272.45 

58.51 

'& 

515.72 

80.50 

835.97 

102.49 

.$. 

276.12 

58.90 

.a 

J620.77 

80.90 

842.39 

102.89 

•I 

279.81 

59.30 

•8 

525.84 

81.29 

848.83 

103.28 

19. 

283.53 

59.69 

26. 

530.93 

81.68 

33. 

855.30 

103.67 

287.27 

60,08 

4 

536.05 

82.07 

861.79 

104.06 

J  , 

291.04 

60.48 

1 

541.19 

82.47 

868.30 

104.46 

J  . 

294.83 

60.87 

i 

546.36 

82.86 

874.84 

104.85 

,.  . 

298.65 

61.26 

4|  551.55 

83.25 

881  .41 

105.24 

m.  . 

302.49 

61.65 

.1  i  556.76 

83.64 

888. 

105.64 

306.35 

62.05 

.£!  562. 

84.04 

894.62 

106.03 

4 

310.25   62.44 

.1  567.27 

84.43 

901.25 

106.42 

20. 

314.16   62.83 

27. 

572.50 

84.82 

34. 

907.92 

106.81 

•i 

318.10  |  63,22 

•i 

577.87 

85.21 

1 

914.61 

107.21 

.1 

322.06  |  63.62 

.4  583.21 

85.61 

,1 

921.32 

107.60 

•8 

326.05 

64.01 

.11  588.57 

86. 

•8 

928.06 

107.99 

•if 

330.06 

64.40 

.-|i  593.96 

86.39 

i 

934.82 

108.39 

•y 

334.10 

64.79 

•w 

599.37 

86.79 

•1 

941.60 

108.78 

.£ 

338.16 

65.19 

604.81 

87.18 

i 

948.42 

109.17 

.1 

342.25 

65.58 

1 

610.27 

87.57 

•¥ 

955.25 

109.56 

21. 

346.36 

65.97 

28. 

615.75 

87.96 

35. 

962.11 

109.96 

.. 

350.50 

66.37 

•i 

621.26 

88.36 

.1 

968.99 

110.35 

.j 

354.66 

66.76 

.i 

626.80 

88.75 

^i 

975.91 

110.74 

.. 

358.84 

67.15 

•1 

632.36 

89.14 

•8 

982.84 

111.13 

363.05 

67.54 

4 

637.94 

89.54 

.1 

989.80 

111.53 

367.28 

67.94 

•i" 

643.55 

89.93 

.|  !  996.78 

111.92 

371.54 

68.33 

.1]  649.18 

90.32 

.f  1003.79 

112.31 

. 

375.83 

68.72 

•f 

654.84 

90.71 

4  1010.80 

112.70 

22. 

380.13 

69.12 

29. 

660.52 

91.11 

36.  1017.88 

113.10 

.. 

384.46 

69.51 

.1 

666.23 

91.50 

4  1024.95 

113.49 

388.82 

69.90 

.-  . 

i  671.96 

91.89 

.1 

1032.06 

113.88 

393.20 

70.29 

j 

i  677.71 

92.28 

J 

1039.19 

114.28 

397.61 

70.69 

,:  , 

683.49 

92.68 

3, 

1046.35 

114.67 

t. 

402.04 

71.08 

J 

689.30 

93.07 

j 

1053.52 

115.06 

,; 

406.49 

71.47 

J 

695.13 

93.46 

_j. 

1060.73 

115.45 

. 

410.97   71.86 

4 

700.98   93.85 

1067.95 

115.85 

AREAS    AND    CIRCUMFERENCES    OF    CIRCLES. 


TABLE— (Continued). 


Dinm.  ]   Area.     Circum.  a  Diam. 

Area. 

Circum. 

Diam.    Are:v.     Circum. 

37.  |  1075.2 

116.2 

44. 

1520.5 

138.2 

51.   2042.8 

160.2 

ii  1082.5 

116.6 

4 

1529.2 

138.6 

.4  2052.8 

160.6 

1089.8 

11-7. 

.1 

1537.9 

139. 

.2  2062.9 

161. 

1097.1 

117.4 

ti 

1546.5 

139.4 

.1  2072.9 

161.3 

1104.5 

117.8 

.1 

1555.3 

139.8 

.2  2083.1 

161.8 

1111.8 

118.2 

•I 

1564. 

140.2 

.|  2093.2 

162.1 

1119.2 

118.6 

.3. 

1572.8 

140.6 

.f  2103.3 

162.6 

1126.7 

119. 

'ii 

1581.6 

141. 

.f  i  2113.5 

162.9 

38. 

1134.1 

119.4 

45. 

1590.4 

141.4 

52.   2123.7 

163.4 

1141.6 

119.8 

1 

1599.3 

141.8 

.1  2133.9 

163.7 

1149.1 

120.2 

1 

1608.2 

142.2 

i  !  2144.2 

164.1 

1156.6 

120.6 

•1 

1617. 

142.6 

.1  !  2154.4 

164.5 

1164.2 

121. 

i 

1626. 

142.9 

.2  !  2164.8 

164.9 

1171.7 

121.3 

4 

1634.9 

143.3 

.1  2175. 

165.3 

1179.3 

121.7 

1 

1643.9 

143.7 

.f  2185.4 

165.7 

1186.9 

122.1 

•t 

1652.9 

144.1 

.1]  2195.7 

166.1 

39. 

1194.6 

122.5 

46. 

1661.9 

144.5 

53.   2206.2 

166.5 

1202.3 

122.9 

4 

1671. 

144.9 

.4  2216.6 

166.8 

[1 

1210. 

123.3 

i 

1680. 

145,3 

.4  !  2227. 

167.3 

t 

1217.7 

123.7 

'! 

1689.1 

145.7 

.41  2237.5 

167.6 

1 

1225.4 

124.1 

4 

1698.2 

146.1 

.4  2248. 

168.1 

•k 

1233.2 

124.5 

£ 

1707.4 

146.5 

1  2258.5 

168.4 

.2. 

1241  . 

124.9 

•f 

1716.5 

146.9 

.f  .2269. 

168.9 

.1 

1248.8 

125.3 

,1 

1725.7 

147.3 

.1  2279.6 

169.2 

40. 

1256.6 

125.6 

47. 

1734.9 

147.7 

54.   2290.2 

169.6 

4 

1264.5 

126. 

•I 

1744.2 

148. 

.4  2300.8 

170. 

.1 

1272.4 

126.4 

I 

1753.5 

148.4 

.4  2311.5 

170.4 

;j 

1280.3 

126.8 

1 

1762.7 

148.8 

.|  2322.1 

170.8 

.1 

1288.2 

127.2 

1 

1772.1 

149.2 

.4  2332.8 

171.2 

,|. 

1296.2 

127.6 

•1? 

1781.4 

149.6 

.4  2343.5 

171.6 

s 

1304.2 

128. 

.f  i  1790.8 

150. 

.1  2354.3 

172. 

.2. 

1312.2 

128.4 

I 

1800.1 

150.4 

,|  2365. 

172.3 

41. 

1320.3 

128.8 

48. 

1809.6 

150.8 

55.   2375.8 

172.8 

1328.3 

129.2 

i 

1819. 

151.2 

4  2386.6 

173.1 

1336.4 

129.6 

1 

1828.5 

151.6 

.|!  2397.5 

173.6 

1344.5 

130. 

'1 

1837.9 

152. 

.1  2408.3 

173.9 

1352.7 

130.4 

1847.5 

152.4 

.2  2419.2 

174.4 

1360.8 

130.8 

1857. 

152.8 

.*'  2430.1 

174.7 

1369. 

131.2 

1866.5 

153.2 

.1  i  2441. 

175.1 

1377.2 

131.6 

•¥ 

1876.1 

153.5 

.|  2452. 

175.5 

42. 

1385.4 

131.9 

1885.7 

153.9 

56.   2463. 

175.9 

.1 

1393.7 

132.3 

1 

1895.4. 

154.3 

1!  2474. 

176.3 

i 

1402. 

132.7 

I  1905. 

154.7 

2485. 

176.7 

•8 

1410.3 

133.1 

\  1914.7 

155.1 

2496.1 

177.1 

.-1 

1418.6 

133.5 

t'.  . 

1  1924.4 

155.5 

2507.2 

177.5 

•f 

1427. 

133.9 

!  1934.1 

155.9 

:  2518.2 

177.8 

.4 

1435.4 

134.3 

1943.9 

156.3 

.4  2529.4 

178.3 

•8 

1443.8 

134.7 

1953.7 

156.7 

4!  2540.5 

178.6 

43. 

1452.2 

135.1 

50  ! 

1963.5 

157.1 

57.   2551.8 

179.1 

.:  . 

1460.6 

135.5 

1973.3 

157.4 

!  2562.  9 

179.4 

1469.1 

135.9 

1983.2 

157.9 

•  2574.2 

179.9 

1477.6 

136.3 

1993. 

158.2 

2585.4 

180.2 

1486.2 

136.7 

2003. 

158.7 

2596.7 

180.6 

1494.7 

137.1 

2012.8 

159. 

1  2608. 

181. 

1503.3 

137.4 

2022.8 

159.4 

..  2619.4 

181.4 

•v 

1511.9 

137.8 

2032.8 

159.8 

.|  1  2630.7 

181.8 

AREAS    AND    CIRCUMFERENCES    OP    CIRCLES. 


TABLE — (Continued). 


Diam. 

Area. 

Circum. 

Diam. 

Area. 

Circum. 

Diam. 

Area.   i 

Circum. 

58 

2642.1 

182.2 

)5. 

3318.3 

204.2 

72. 

4071.5 

226.2 

2653.4 

182.6 

•i 

3331. 

204.5 

4 

4085.6 

226.5 

. 

2664.9 

183. 

.1 

3343.9 

205. 

4 

4099.8 

227. 

i 

2676.3 

183.3 

•8 

3356.7 

205.3 

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4114. 

227.3 

t.  [ 

2687.8 

183.8 

•a 

3369.6 

205.8 

'! 

4128.2 

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* 

2699.3 

184.1 

•f 

3382.4 

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£  i 

4142.5 

228.1 

[ 

2710.9 

184.6 

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3395.3 

206.6 

•i  i 

4156.8 

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]  I 

2722.4 

184.9 

i 

3408.2 

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i 

4171. 

228.9 

59 

2734. 

185.4 

66. 

3421.2 

207.3 

73. 

4185.4 

229.3 

i 

2745.5 

185.7 

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4 

4199.7 

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[ 

2757.2 

186.1 

i 

3447.2 

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2768.8 

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3473.2 

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m  i 

2792.2 

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3499.4 

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2815.6 

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4286.3 

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67. 

3525.6 

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74. 

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3552. 

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2862.8 

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•8 

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4344.5 

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e  i. 

2874.8 

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•1 

3578.5 

212.1 

4359.2 

234. 

.  j. 

2886.6 

190.4 

*t 

3591.7 

212.4 

4373.8 

234.4 

m  i 

2898.5 

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4 

3605. 

212.8 

4388.5 

234.8 

.  ' 

2910.6 

191.2 

7 
•  •g1 

3618.3 

213.2 

4403.1 

235.2 

Gl 

2922.5 

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68. 

3631.7 

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75. 

4417.9 

235.6 

2934.4 

192. 

•i 

3645. 

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•I 

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4447. 

237.2 

i  2982.6 

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•f 

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237.5 

2994.8 

194. 

•f 

3712.2 

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4506.7 

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i  3006.9 

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3725.7 

216.3 

4521.5 

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62 

3019.1 

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69. 

3739.3 

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76. 

4536.5 

238.8 

3031.2 

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4 

4551.4 

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.  L 

3043.5 

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i 

3766.4 

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.t 

4566.4 

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4581.3 

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3068. 

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218.3 

4596.3 

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3080.2 

196.7 

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4611.3 

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3. 

3092.6 

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3821. 

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63 

3117.2 

197.9 

70. 

3848.5 

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77. 

4656.6 

241.9 

3129.6 

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•i 

3862.2 

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•i 

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242.2 

3142. 

198.7 

i 

3876. 

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4686.9 

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3154.4 

199. 

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'I 

4702.1 

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3166.9 

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f 

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J 

4732.5 

243.8 

3191.9 

200.3 

iX 

3931.4 

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3204.4 

200.6 

i 

3945.2 

222.6 

•1 

4763. 

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64 

3217. 

201.1 

71.  a 

3959.2 

223. 

78. 

4778.4 

245. 

3229.5 

201.4 

.1 

3973.1 

223.4 

4793.7 

245.4 

3242.2 

201.8 

i 

3987.1 

223.8 

4809. 

245.8 

.  3254.8 

202.2 

•1 

4001.1 

224.2 

4824.4 

246.2 

3267.5 

202.6 

.1 

4015.2 

224.6 

4839.8 

246.6 

3280.1 

203. 

.  ir 

4029.2 

225. 

4855.2 

247. 

3292.8 

203.4 

:l 

4043.3 

225.4 

4870.8 

247.4 

i  3305.5 

203.8 

•J 

4057.4 

225.8 

4886.1 

247.7 

AREAS   AND    CIRCUMFERENCES    OF    CIRCLES. 

TABLE — (Continued). 


Diam.  |   Area.    Circum. 

Piam.  !   Area. 

Circutn. 

Diam. 

Area. 

Circum. 

79. 

4901.7 

248.2 

86.   :  5808.8 

270.2 

93. 

6792.9 

292.2 

4 

4917.2 

248.5 

4  5825.7 

270.5 

•i 

6811.1 

292.6 

4932.7 

249. 

.i-  5842.6 

271. 

.5 

6829.5 

293. 

..« 

4948.3 

249.3 

.|  5859.5 

271.3 

•  ~8 

6847.8 

293.4 

i 

4963.9 

249.8 

.i  5876.5 

271.7 

.1 

6866.1 

293.7 

•t 

4979.5 

250.1 

.4  ;  5893.5 

272.1 

•! 

6884.5 

294.1 

4995.2 

250.5 

.f  !  5910.6 

272.5 

S. 

*  4 

6902.9 

294.5 

5010.8 

250.9 

4  5927.6 

272.9 

3 

6921.3 

294.9 

so!8 

5026.5 

251.3 

87.  !  5944.7 

273.3 

94. 

6939.8 

295.3 

15042.2 

251.7 

|!  £961.7 

273.7 

.1 

6958.2 

295.7 

5058. 

252.1 

5978.9 

274.1 

.1 

6976.7 

296.1 

5073.7 

252.5 

5996. 

274  .4 

•1 

6995.2 

296.5 

5089.6 

252.9 

i  6013.2 

274.9 

•f 

7013.8 

296.9 

5105.4 

253.3 

;  6030.4 

275.2 

•t 

7032.3 

297.3 

5121.2 

253.7 

.4  6047.6 

275.7 

3. 
•  4 

7051. 

297.7 

5137.1 

254.1 

.f  1  6064.8 

276. 

4 

7069.5 

298.1 

81. 

5153. 

254.5 

88. 

6082.1 

276.5 

95. 

7088.2 

298.5 

.1 

5168.9 

254.9 

4 

6099.4 

276.8 

.1 

7106.9 

298.8 

.0. 

5184.9 

255.3 

.1 

6116.7 

277.2 

.1 

7125.6 

299.2 

•1 

5200.8 

255.6 

'! 

6134. 

277.6 

•¥ 

7144.3 

299.6 

.1 

5216.8 

256. 

,j  i 

6151.4 

278. 

1 

7163. 

300. 

•f 

5232.8 

256.4 

^  1  . 

6168.8 

278.4 

| 

7181.8 

300.4 

•f 

5248.9 

256.8 

,4. 

6186.2 

278.8 

.1 

7200.6 

300.8 

7 

5264.9 

257.2 

I. 

6203.6 

279.2 

*  ft" 

7219.4 

301.2 

82! 

5281. 

257.6 

89. 

6221.1 

279.6 

96. 

7238.2 

301.6 

•1 

5297.1 

258. 

4 

6238.6 

280. 

.1 

7257.1 

302. 

.1 

5313.3 

258.4 

i 

•  A 

6256.1 

280.4 

i 

7276. 

302.4 

•1 

5329.4 

258.8 

.1 

6273.6 

280.8 

•1 

7294.9 

302.8 

»f 

5345.6 

259.2 

.i 

6291.2 

281.2 

•i 

7313.8 

303.2 

J 

5361.8 

259.6 

•1 

6308.8 

281.6 

•f 

7332.8 

303.5 

*f 

5378.1 

260. 

•f 

6326.4 

282. 

.| 

7351.8 

303.9 

•8 

5394.3 

260.4 

•8 

6344. 

282.3 

•1 

7370.7 

304.3 

83. 

5410.6 

260.8 

90. 

6361.7 

282.7 

97. 

7389.8 

304.7 

.1 

5426.9 

261.1 

•i 

6379.4 

283.1 

•1 

7408.8 

305.1 

•I 

5443.3 

261.5 

.-i- 

6397.1 

283.5 

i 

7428. 

305.5 

•1 

5459.6 

261.9 

•1 

6414.8 

283.9 

•1 

7447. 

305.9 

i 

5476. 

262.3 

4 

6432.6 

284.3 

.i 

7466.2 

306.3 

•1 

5492.4 

262.7 

•f 

6450.4 

284.7 

•t 

7485.3 

306.7 

£ 

5508.8 

263.1 

•  f 

6468.2 

285.1 

3. 
*  4 

7504.5 

307.1 

•f 

5525.3 

263.5 

•8 

6486. 

285.5 

•1 

7523.7 

307.5 

84. 

5541.8 

263.9 

91. 

6503.9 

285.9 

98. 

7543. 

307.9 

4 

5558.3 

264.3 

4  6521.7 

286.3 

7562.2 

308.3 

I 

5574.8 

264.7 

.|  6539.7 

286.7 

7581.5 

308.7 

•1 

5591.3 

265. 

6557.6 

287.1 

7600.8 

309. 

.i 

5607.9 

265.5 

•  3 

6575.5 

287.5 

7620.1 

309.4 

.1 

5624.5 

265.8 

6593.5 

287.8 

7639.4 

309.8 

.3. 

5641.2 

266.2 

3. 

6611.5 

288.2 

1 

7658.9 

310.2 

i 

5657.8 

266.6 

1 

6629.5 

288.6 

]f 

7678.2 

310.6 

85. 

5674.5 

267. 

92!  8 

6647.6 

289. 

99!  8 

7697.7 

311. 

5691.2 

267.4 

4 

6665.7 

289.4 

4 

7717.1 

311.4 

5707.9 

267.8 

i 

6683.8 

289.8 

:  i 

7736.6 

311.8 

t! 

5724.6 

268.2 

i 

6701.9 

290.2 

^1 

7756.1 

312.2 

..  . 

5741.5 

268.6 

6720.1 

290.6 

.1 

7775.6 

312.6 

.. 

5758.2 

268.9 

!-|i  6788.2 

291. 

•f 

7795.2 

313. 

J 

5775.1 

269.4 

.-*-  6756.4 

291.4 

_5. 

7814.8 

313.4 

^ 

5791.9 

269.7 

•I 

6774.7 

291.8 

^i 

7834.3 

313.8 

100  !8 

7854. 

314.2 

10 


AREAS   AND    CIRCUMFERENCES  OF   CIRCLES 


AREAS  AND  CIRCUMFERENCES  OF  CIRCLES  AND  SIDES  OF 
EQUAL  SQUARES, 

FROM  1  TO  50,  FEET   OR  INCHES, 

Advancing-  by  an  inch  or  twelfth  of  an  inch. 


Diam. 

Area. 

Pi                     Side  of 
:um'         Equal  Sq. 

Diam. 

Area. 

Circum. 

;     Side  of 
Equal  Sq. 

1. 

.785 

3.142 

.886 

5. 

19.635 

15.708 

4.431 

.1 

.922 

3.403 

.960 

.1 

20.295 

15.970 

4.505 

.2 

1.069 

3.665 

1.034 

.2 

20,966 

16.232 

4.579 

.3 

1.227 

3.927 

1.107 

.5 

21.643 

16.493 

4.652 

.4 

1.396 

4.189 

1.181 

.4 

22.340 

16.755 

4.726 

.5 

1.576 

4.450 

1.255 

.5 

23.044 

17.017 

4.800 

.6 

1.767 

4.712 

1.329 

.6 

23.758 

17.278 

4.874 

.7 

1.969 

4.974 

1.403 

.7 

24U84 

17.541 

4.945 

.8 

2.181 

5.236 

1.477 

.8 

25.220 

17.802 

5.022 

.9 

2.405 

5.498 

1.550 

.9 

25.967 

18.064 

5.095 

.10 

2.640 

5.760 

1.624 

.10 

26.725 

18.326 

5.169 

.11 

2.885 

6.021 

1.698 

.11 

27.494 

18.588 

5.243 

2. 

3.142 

6.283 

1.772 

6. 

28.274 

18.849 

5.317 

.1 

3.409 

6.545 

1.845 

.1 

29.065 

19.111 

5.391 

.2 

3.687 

6.807 

1.919 

.2 

29.867 

19.373 

5.465 

.3 

3.976 

7.069 

1.994 

.3 

30.680 

19.635 

5.538 

.4 

4.276 

7.330 

2.067 

.4 

31.503 

19.897 

5.612 

.5 

4.587 

7.592 

2.142 

.5 

32.338 

20.159 

5.687 

.6 

4.909 

7.854 

2.215 

.6 

33.183 

20.420 

5.760 

.7 

5.241 

8.116 

2.287 

.7 

34.039 

20.682 

5.834 

.8 

5.585 

8.378 

2.363 

.8 

34.907 

20.944 

5.908 

.9 

5.940 

6L639 

2.437 

.9 

35.785 

21  .  206 

5.982 

.10 

6.305 

srapi 

2.511 

.10 

36.674 

21.468 

6.056 

.11 

6.681 

9.168 

2.584 

^.11 

37.574 

21.729 

6.130 

3. 

7.069 

9.  42^ 

2.658 

7. 

38.485 

21.991 

6.203 

.1 

7.467 

9.687, 

2.731 

.1 

39.406 

22.253 

6.278 

.2 

7.876 

9.948 

2.806 

.2 

40.339 

22.515 

6.352 

.3 

8.296 

10.210 

2.880 

.3 

41.283 

22.777 

6.425 

.4 

8.727 

10.472 

2.953 

.4 

42.237 

23.038 

6.499 

.5 

9.168 

10.734 

3.027 

.5 

43.202 

23.300 

6.573 

.6 

9.621 

10.996 

3.101 

.6 

44.179 

23.562 

6.646 

.7 

10.085 

11.257 

3.175 

.7 

45.166 

23.824 

6.721 

.8 

10.559 

11.519 

3.249 

.8 

46.164 

24.086 

6.745 

.9 

11.045 

11.781 

3.323 

.9 

47.173 

24.347 

6.868 

.10 

11.541 

12.042 

3.397 

.10 

48.193 

24.609 

6.942 

.11 

12.048 

12.305 

3.471 

.11 

49.224 

24.871 

7.016 

4. 

12.566 

12.566 

3.544 

8. 

50.266 

25.133 

7.089 

.1 

13.095 

12.828 

3.618 

.1 

51.318 

25.395 

7.164 

.2 

13.635 

13.090 

3.692 

.2 

52.382 

25.656 

7.238 

.3 

14.  186 

13.352 

3.766 

.3 

53.456 

25.918 

7.311 

.4 

14.748 

13.614 

3.840 

.4 

54.541 

26.180 

7.385 

.5 

15.321 

13.875 

3.913 

.5 

55.638 

26.442 

7.459 

.6 

15.904 

14.137 

3.988 

.6 

56.745 

26.704 

7.532 

.7 

16.499 

14.399 

4.061 

.7 

57.863 

26.965 

7.606 

.8 

17.104 

14.661 

4.135 

.8 

58.992 

27.227 

7.681 

.9 

17.720 

14.923 

4.209 

.9 

60.132 

27.489 

7.754 

.10 

18.348 

15.184 

4.283 

.10 

61.283 

27.750 

7.828 

.11 

18.985 

15.446 

4.357 

.11 

62.445 

28.013 

7.902 

AND    SIDES    OF    EQUAL   SQUARES. 


11 


TABLE— (Continued). 


Diam, 

Area. 

Circum.    E<lual  gq 

Diuui.  j   Area. 

Circum. 

Side  of 
Equal  Sq. 

9. 

63.617 

28.274   7.976 

13.6   143,139 

42.412 

11.964 

.1 

64.801 

28.536   8.050 

.7  !  144,911 

42.673 

12.038 

.2 

65.995 

28.796 

8.124 

.8 

146.695 

42.935 

12.112 

.3 

67.201 

29.060 

8.197 

.9 

148.490 

43.197 

12.185 

.4 

68.417 

29.322 

8.272 

.10 

150,294 

43.459 

12.259 

.5 

69.644 

29.583 

8.346 

.11 

152.111 

43.721 

12.333 

.6 

70.882 

29.845 

8.419 

14. 

:  153.  938 

43.982 

12.407, 

.7 

72.131 

30.107 

8.493 

.l-? 

•  155.776 

44.244 

12.481 

.8 

73.391 

30.369 

8.567 

.2 

157.625 

44.506 

12.554 

.9 

74.662 

30.631 

8.640 

'.3 

159.485 

44.768 

12.628 

.10 

75.943 

30.892 

8.715 

A 

161.355 

45.030 

12.702 

.11 

77.236 

31.154 

8.789 

.5 

163.237 

45.291 

12.776 

10. 

78.540 

31.416 

8.862 

,6  |  165.130 

45.553 

12.850 

.1 

79.854 

31.678 

8.936 

•  7 

167.033 

45.815 

12.924 

.2 

81.180 

31.940 

9.010 

.8 

168.948 

46.077 

12.997 

.3 

82.516 

32.201 

9.083 

.9 

170.874 

46.339 

13.071 

.4 

83.863 

32.4§3 

9.158 

.10 

172.809 

46.600 

13.145 

.5 

85.221 

32.725 

9.232 

.11 

174.757 

46.862 

13.219 

.6 

86.590 

32.987 

9.305 

15. 

176.715 

47.124 

13.293 

.7 

87.970 

33.249 

9.379 

.1 

178.683 

47.386 

13.367 

.8 

89.361 

33.510 

9.453 

.2 

180.663 

47.648 

13.441 

.9 

90.763 

33.772 

9.526 

.3 

182.655 

47.909 

13.514 

.10 

92.175 

34.034 

9.601 

.4 

184.656 

48.171 

13.588 

.11 

93.599 

34.296 

9.674 

.5 

186.668 

48.433 

13.662 

11. 

95.033 

34.558 

9.748 

.6 

188.692 

48.695 

13.736 

.1 

96.478 

34.819 

9.822 

.7 

190.726 

48.957 

13.810 

.2 

97.935 

35.081 

9.896 

.8 

192.772 

49.218 

13.884 

'.B 

99.402 

35.343 

9.970 

.9 

194.828 

49.480 

13.958 

.4 

100.880 

35.605 

10.044 

.10 

196.895 

49.742 

14.032 

.5 

102.369 

35.867 

10.118 

.11 

198.973 

50.004 

14.106 

.6 

103.869 

36.128 

10.191 

16. 

201.062 

50.266 

14.179 

.7 

105.379 

36.390 

10.265 

.1 

203.162 

50.527 

14.253 

.8 

106.901 

36.652 

10.339 

.2 

205.273 

50.789 

14.327 

.9 

108.434 

36.914 

10.413 

.3 

207.395 

51.051 

14.401 

.10 

109.977 

37.176 

10.488 

.4 

209.526 

51.313 

14.475 

.11 

111.532 

37.437 

10.562 

.5 

211.670 

51.575 

14.549 

12. 

113.098 

37.699 

10.634 

.6 

213.825 

51.836 

14.622 

.1 

114.673 

37.961 

10.709 

.7 

215.990 

52.098 

14.696 

.2 

116.261 

38.223 

10.783 

.8 

218.166 

52.360 

14.770 

'.3 

117.860 

38.485 

10.856 

.9 

220.354 

52.622 

14.844 

A 

119.467 

38.746 

10.930 

.10 

222.551 

52.884 

14.918 

.5 

121.088 

39.008 

11.004 

.11 

224.760 

53.145 

14.991 

.6 

122.719 

39.270 

11.077 

17. 

226.981 

53.407 

15.065 

.7 

124.360 

39.532 

11.151 

.1 

229.211 

53.669 

15.139 

.8 

126.013 

39.794 

11.225 

.2 

231.453 

53.931 

15.213 

.9 

127.677 

40.055 

11.299 

'.3 

233.706 

54.193 

15.287 

.10 

129.350 

40.317 

11.373 

A 

235.968 

54.454 

15.360 

.ll|  131.036 

40.579 

11.447 

.5 

238.243 

54.716 

15.434 

13. 

132.733 

40.841 

11.520 

.6 

240.529 

54.978 

15.508 

.1 

134.439 

41.103 

11.594 

.7 

242.824 

55.240 

15.582 

.2 

136.157 

41.364 

11.668 

.8 

245.132 

55.502 

15.656 

.3 

137.887 

41.626 

11.742 

.9 

247.450 

55.763 

15.730 

.4 

139.626 

41.888 

11.816 

.10 

249.778 

56.025 

15.804 

.5 

141.377   42.150 

11.889 

.11 

252.118 

56.287 

15.878 

12 


AREAS    AND    CIRCUMFERENCES    OF    CIRCLES 


TABLE — (Continued). 


Diam. 

Area. 

Circum. 

Side  of 
E^ual  Sq. 

Diam. 

Area. 

Circum. 

Side  of 
Equal  Sq, 

18. 

254.470 

56.549 

15.952 

22.6 

397.609 

70.686 

19.940 

.1 

256.830 

56.811 

16.026 

.7 

400.558 

70.948 

20.014 

.2 

259.203 

57.072 

16,100 

.8 

403.520 

71.210 

20.088 

.3 

261.587 

57.334 

16.173 

.9 

406.494 

71,471 

20.161 

.4 

263.981 

57.596 

16.247 

.10 

409.476 

71.733 

20.235 

.5 

266.386 

57.858 

16.321 

.11 

412.471 

71.995 

20.309 

.6 

268.803 

58.120 

16.395 

23. 

415.477 

72.257 

20.383 

.7 

271.229 

58.381 

16.469 

.1 

418.492 

72.519 

20.457 

.8 

273.668 

58.643 

16.543 

.2 

421.519 

72.780 

20.530 

.9 

276.117 

58.905 

16.616 

.3 

424.558 

73.042 

20.604 

.10 

278.576 

59.167 

16.690 

.4 

427.606 

73.304 

20.678 

.11 

281.047 

59.429 

16.764 

.5 

430.666 

73.566 

20.752 

19. 

283.529 

59.690 

16.838 

.6 

433.737 

73.828 

20.826 

.1 

286.021 

59.952 

16.911 

.7 

436.818 

74.089 

20.900 

.2 

288.525 

60.214 

16.985 

.8 

439.911 

74.351 

20.974 

.3 

291.040 

60.476 

17.059 

.9 

443.015 

74.613 

21.047 

.4 

293.564 

60.738 

17.133 

.10 

446.128 

74.875 

21.121 

.5 

296.101 

60.999 

17.207 

.11 

449.254 

75.137 

21.195 

.6 

298.648 

61.261 

17.281 

24. 

452.390 

75.398 

21.269 

.7 

301.205 

61.523 

17.355 

.1 

455.536 

75.660 

21.343 

.8 

303.775 

61.785 

17.429 

.2 

458.695 

75.922 

21.417 

.9 

306.355 

62.047 

17.502 

.3 

461.864 

76.184 

21.491 

.10 

308.945 

62.308 

17.576 

.4 

465.043 

76.446 

21.565 

.11 

311.547 

62.570 

17.650 

.5 

468.234 

76.707 

21.639 

20. 

314.160 

62.832 

17.724 

.6 

471.436 

76.969 

21.712 

.1 

316.782 

63.094 

17.798 

.7 

474.648 

77.231 

21.786 

.2 

319.417 

63.356 

17.871 

.8 

477.872 

77.493 

21.860 

.3 

322.063 

63.617 

17.946 

.9 

481.107 

77.755 

21.934 

.4 

324.718 

63.879 

18.020 

.10 

484.351 

78.016 

22.007 

.5 

327.386 

64.141 

18.094 

.11 

487.607 

78.278 

22.081 

.6 

330.064 

64.403 

18.167 

25. 

490.875 

78.540 

22.155 

.7 

332.752 

64.665 

18.241 

.1 

494.152 

78.802 

22.229 

.8 

335.453 

64.926 

18.315 

.2 

497.441 

79.064 

22.302 

.9 

338.164 

65.188 

18.389 

.3 

500.742 

79.325 

22.377 

.10 

340.884 

65.450 

18.463 

.4 

504.051 

79.587 

22.450 

.11 

343.617 

65.712 

18.536 

.5 

507.373 

79.849 

22.524 

21. 

346.361 

65.974 

18.610 

.6 

510.706 

80.111 

22.598 

.1 

349.115 

66.235 

18.684 

.7 

514.048 

80.373 

22.672 

.2 

351.880 

66.497 

18.758 

.8 

517.403 

80.634 

22.746 

.3 

354.657 

66.759 

18.832 

.9 

520.769 

80.896 

22.820 

.4 

357.443 

67.021 

18.906 

.10 

524.144 

81.158 

22.894 

.5 

360.241 

67.283 

18.980 

.11 

527.532 

81.420 

22.968 

.6 

363.051 

67.544 

19.053 

26. 

530.930 

81.682 

23.041 

.7 

365.870 

67.806 

19.127 

.1 

534.338 

81.943 

23.115 

.8 

368.701 

68.068 

19.201 

.2 

537.758 

82.205 

23.189 

.9 

371.543 

68.330 

19.275 

.3 

541.190 

82.467 

23.263 

.10 

374.395 

68.592 

19.349 

.4 

544.630 

82.729 

23.337 

.11 

377.259 

68.853 

19.422 

.5 

548.083 

82.991 

23.411 

22. 

380.134 

69.115 

19.496 

.6 

551.547 

83.252 

23.485 

.1 

383.018 

69.377 

19.570 

.7 

555.020 

83.514 

23.558 

.2 

385.914 

69.639 

19.644 

.8 

558.506 

83.776 

23.632 

.3 

388.822 

69.901 

19.718 

.9 

562.003 

84.038 

23.706 

.4 

391.739 

70.162 

19.791 

.10 

565.508 

84.300 

23.780 

.5 

394.668 

70.424 

19.865 

.11 

569.027 

84.561 

23.853 

AND    SIDES    OF   EQUAL    SQUARES. 


13 


TABLE — (Continued). 


T)i«:n. 

Area. 

Circum. 

Side  of 
Equal  Sq. 

Diaui. 

Area. 

Circum. 

Side  of 
Equal  Sq. 

27, 

572.557 

84.823 

23.928 

31.6 

779.313 

98.960 

27.916 

.1 

576.095 

85.085 

24.001 

.7 

783.440 

99.222 

27.990 

.2 

579.646 

85.347 

24.075 

.8 

787.581 

99.484 

28.064 

.3 

583.209 

85.609 

24.149 

.9 

791.732 

99.746 

28.137 

.4 

586.780 

85.870 

24.223 

.10 

795.892 

100.008 

28.211 

.5 

590.364 

86.132 

24.297 

.11 

800.065 

100.269 

28.285 

.6 

593.959 

86.394 

24.371 

32. 

804.250 

100.531 

28.359 

.7 

597.563 

86.656 

24.445 

.1 

808.442 

100.793 

28.433 

.8 

601.179 

86.918 

24.519 

.2 

812.648 

101.055 

28.507 

.9 

604.807 

87.179 

24.592 

.3 

816.865 

101.317 

28.580 

.10 

608.444 

87.441 

24.666 

.4 

821.090 

101.578 

28.654 

.11 

612.093 

87.703 

24.740 

.5 

825.329 

101.840 

28.728 

28. 

615.754 

87.965 

24.814 

.6 

829.579 

102.102 

28.802 

.1 

619.423 

88.227 

24.888 

.7 

833.837 

102.364 

28.876 

.2 

623.105 

88.488 

24.961 

.8 

838.108 

102.626 

28.950 

.3 

626.798 

88.750 

25.035 

.9 

842.391 

102.887 

29.023 

.4 

630.500 

89.012 

25.109 

.10 

846.681 

103.149 

29.097 

.5 

634.215 

89.274 

25.183 

.11 

850.986 

103.411 

29.171 

.6 

637.941 

89.536 

25.257 

33. 

855.301 

103.673 

29.245 

.7 

641.676 

89.797 

25.331 

.1 

859.624 

103.935 

29.319 

.8 

645.424 

90.059 

25.405 

.2 

863.961 

104.196 

29.392 

.9 

649.182 

90.321 

25.479 

.3 

868.309 

104.458 

29.467 

.10 

652.950 

90.583 

25.552 

.4 

872.665 

104.720 

29.541 

.11 

656.730 

90.845 

25.626 

.5 

877.035 

104.982 

29.615 

29. 

660.521 

91.106 

25.700 

.6 

881.415 

105.244 

29.688 

.1 

664.321 

91.368 

25.774 

.7 

885.804 

105.505 

29.762 

2 

668.135 

91.630 

25  .848 

.8 

890.206 

105.767 

29.836 

.3 

671.959 

91.892 

25.922 

.9 

894.620 

106.030 

29.910 

.4 

675.792 

92.154 

25.996 

.10 

899.041 

106.291 

29.984 

.5 

679.638 

92.415 

26.070 

.11 

903.476 

106.553 

30.058 

.6 

683.494 

92.677 

26.143 

34. 

907.922 

106.814 

30.131 

.7 

687.360 

92.939 

26.217 

.1 

912.377 

107.076 

30.205 

.8 

691.239   93.201 

26.291 

.2 

916.845 

107.338 

30.279 

.9 

695.128   93.463 

26.365 

.3 

921.323 

107.600 

30.353 

.10 

699.626   93.724 

26.439 

.4 

925.810 

107.862 

30.427 

.11 

702.938   93.986 

26.513 

.5 

930.311 

108.123 

30.501 

30. 

706.860 

94.248 

26.586 

.6 

934.822 

108.385 

30.574 

.1 

710.791 

94.510 

26.660 

.7 

939.342 

108.647 

30.648 

.2 

714.735 

94.772 

26.734 

.8 

943.875 

108.909 

30.722 

.3 

718.690 

95.033 

26.808 

.9 

948.420 

109.171 

30.796 

.4 

722.654 

95.295 

26.882 

.10!  952.972 

109.432 

30.870 

.5 

726.631 

95.557 

26.956 

.11;  957.538 

109.694 

30.944 

.6 

730.618 

95.819 

27.029 

35. 

962.115 

109.956 

31.017 

.7 

734.615 

96.081 

27.103 

.1 

966.700 

110.218 

31.091 

,8 

738.624  !  96.342 

27.177 

.2 

971.299 

110.480 

31.165 

.9 

742.645   96.604 

27.251 

.'3   975.909 

110.741 

31.239 

.10 

746.674  |  96.866 

27.325 

.4  j  980.526 

111.003 

31.313 

.11 

750.716  '  97.128 

27.399 

« 
.O 

985.158 

111.265 

31.386 

31. 

754.769 

97.390 

27.473 

.6 

989.800 

111.527 

31.461 

.1 

758.831 

97.651 

27.547 

.7 

994.451 

111.789 

31.534 

.2 

762.906 

97.913 

27.621 

.8 

999.115 

112.050 

31.608 

.3 

766.992 

98.175 

27.694 

.9 

1003.790 

112.312 

31.682 

.4 

771  .087 

98.437 

27.768 

.10 

1008.474 

112.574 

31.756 

.5 

775.194 

98.699 

27.842 

.11 

1013.171 

112.836 

31.829 

14 


AREAS   AND    CIRCUMFERENCES    OF   CIRCLES 


TABLE — (Continued). 


Diam. 

Area. 

Circum. 

Side  of 
Equal  Sq. 

Diam. 

Area. 

Circum. 

Side  of 
Equal  Sq. 

36. 

1017.878 

113.098 

31.904 

40.6 

1288.252 

127.235 

35.892 

.1 

1022.594 

113.359 

31.978 

.7 

1293.557 

127.497 

35.966 

.2 

1027.324 

113.621 

32.052 

.8 

1298.876 

127.758 

36.039 

.3 

1032.065 

113.883 

32.125 

.9 

1304.206 

128.020 

36.113 

.4 

1036.813 

114.145 

32.199 

.10 

1309.543 

128.282 

36.187 

.5 

1041.576 

114.407 

32.273 

.11 

1314.895 

128.544 

36.261 

.6 

1046.349 

114.668 

32.347 

41. 

1320.257 

128.806 

36.335 

.7 

1051.131 

114.930 

32.421 

.1 

1325.628 

129.067 

36.408 

.8 

1055.926 

115.192 

32.494 

.2 

1331.012 

129.329 

36.482 

.9 

1060.732 

115.454 

32.568 

.3 

1336.407 

129.591 

36.556 

.10 

1065.546 

115.776 

32.642 

.4 

1341.810 

129.  85a 

36.630 

.11 

1070.374 

115.977 

32.716 

.5 

1347.227 

130.115 

36.704 

37. 

1075.213 

116.239 

32.790 

.6 

1352.655 

130.376 

36.778 

.1 

1080.059 

116.501 

32.863 

.7 

1358.091 

130.638 

36.852 

.2 

1084.920 

116.763 

32.937 

.8 

1363.541 

130.900 

36.926 

.3 

1089.792 

117.025 

33.011 

.9 

1369.001 

131.162 

36.999 

.4 

1094.671 

117.286 

33.085 

.10 

1374.470 

131.424 

37.073 

.5 

1099.564 

117.548 

33.159 

.11 

1379.952 

131.685 

37.147 

.6 

1104.469 

117.810 

33.233 

42. 

1385.446 

131.947 

37.221 

.7 

1109.381 

118.072 

33.307 

.1 

1390.247 

132.209 

37  .  295 

.8 

1114.307 

118.334 

33.381 

.2 

1396.462 

132.471 

37.369 

.9 

1119.244 

118.595 

33.455 

.3 

1401.988 

132.733 

37.443 

.10 

1124.189 

118.857 

33.529 

.4 

1407.522 

132.994 

37.517 

.11 

1129.148 

119.119 

33.603 

.5 

1413.070 

133.256 

37.591 

38. 

1134.118 

119.381 

33.676 

.6 

1418.629 

133.518 

37.664 

.1 

1139.095 

119.643 

33.750 

.7 

1424.195 

133.780 

37.738 

.2 

1144.087 

119.904 

33.824 

.8 

1429.776 

1H4.042 

37.812 

.3 

1149.089 

120.166 

33.898 

.9 

1435.368 

1  .'54.  303 

37.886 

.4 

1154.100 

120.428 

33.972 

.10 

1440.967 

134.565 

37.960 

.5 

1159.124 

120.690 

34.045 

.11 

1446.580 

134.827 

38.033 

.6 

1164.159 

120.952 

34.119 

43. 

1452.205 

135.089 

38.107 

.7 

1169.202 

121.213- 

34.193 

.1 

1457.837 

135.351 

38.181 

.8 

1174.259 

121.475 

34.267 

.2 

1463.483 

135.612 

38.255 

.9 

1179.327 

121.737 

34.341 

.3 

1469.140 

135.874 

38.329 

.10 

1184.403 

121.999 

34  .-414 

A 

1474.804 

136.136 

38.402 

.11 

1189.493 

122.261 

34.488 

.5 

M80.483 

136.398 

38.47G 

39. 

1194.593 

122.522 

34.562 

.6 

1486.173 

136.660 

38.550 

.1 

1199.720 

122.784 

34.636 

.7 

1491.871 

136.921 

38.624 

.2 

1204.824 

123.046 

34.710 

.8 

1497.582 

137.183 

38.698 

.3 

1209.958 

123.308 

34.784 

.9 

1503.305 

137.445 

38.772 

.4 

1215.099 

123.570 

34.858 

.10 

1509.035 

137.707 

38.846 

.5 

1220.254 

123.831 

34.932 

.11 

1514.779 

137.969 

38.920 

.6 

1225.420 

124.093 

35.005 

44. 

1520.534 

138.230 

38.993 

.7 

1230.594 

124.355 

35.079 

.1 

1526.297 

138.492 

39.067 

.8 

1235.782 

124.617 

35.153 

.2 

1532.074 

138.754 

39.141 

.9 

1240.981 

124.879 

35.227 

'.S 

1537.862 

139.016 

39.215 

.10 

1246.188 

125.140 

35.301 

.4 

1543.658 

139.278 

39.289 

.11 

1251.408 

125.402 

35.374 

.5 

1549.468 

139.539 

39.363 

40. 

1256.640 

125.664 

35.449 

.6  1555.288 

139.801 

39.437 

.1 

1261.879 

125.926 

35.523 

.7  1561.117 

140.063 

39.511 

.2 

1267.133 

126.188 

35.597 

.8 

1566.960 

140.325 

39.585 

.3 

1272.397 

126.449 

35.670 

.9 

1572.813 

140.587 

39.658 

.4 

1277.669 

126.711 

35.744 

.10 

1578.674 

140.848 

39.732 

.5 

1282.955 

126.973 

35.818 

.11  1584.549  141.110  39.806 

AND    SIDES    OF   EQUAL   SQUARES. 


15 


TABLE — (Continued). 


Dbm. 

Area. 

Circum. 

Side  of 
Equal  Sq. 

Diam. 

Area. 

Circum. 

Side  of 
Equal  Sq. 

45. 

1590.435 

141.372 

39.880 

47.6 

1772.059 

149.226 

42.095 

.1 

1596.329 

141.634 

39.954 

.7 

1778.280 

149.488 

42.169 

.2 

1602.237 

141.896 

40.027 

.8 

1784.515 

149.750 

42.243 

.3 

1608.156 

142.157 

40.101 

.9 

1790.761 

150.011 

42.317 

A 

1614.082 

142.419 

40.175 

.10 

1797.015 

150.273 

42.390 

.5 

1620.023 

142.681 

40.249 

.11 

1803.283 

150.535 

42.464 

.6 

1625.974 

142.983 

40.323 

48. 

1809.562 

150.797 

42.538 

.7 

1631.933 

143.205 

40.396 

.1 

1815.848 

151.059 

42.612 

.8 

1637.907 

143.466 

40.470 

.2 

1822.149 

151.320 

42.686 

.9 

1643.891 

143.728 

40.544 

'.3 

1828.460 

151.582 

42.760 

.10 

1649.883 

143.990 

40.618 

A 

1834.779 

151.844 

42.834 

.11 

1655.889 

144.252 

40.692 

.5 

1841.113 

152.106 

42.908 

46. 

1661.906 

144.514 

40.766 

.6 

1847.457 

152.368 

42.982 

.1 

1667.931 

144.775 

40.840 

.7 

1853.809 

152.630 

43.056 

.2 

1673.970 

145.037 

40.914 

.8 

1860.175 

152.891 

43.130 

.3 

1680.020 

145.299 

40.987 

.9 

1866.552 

153.153 

43.203 

.4 

1686.077 

145.561 

41.061 

.10 

1872.937 

153.415 

43.277 

.5 

1692.149 

145.823 

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153.677 

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1698.231 

146.084 

41.209 

49. 

1885.745 

153.938 

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1704.321 

146.346 

41.283 

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154.200 

43.499 

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41.357 

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154.462 

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146.870 

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1905.037 

154.724 

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1722.663 

147.132 

41.505 

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154.986 

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155.247 

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1924.426 

155.510 

43.868 

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147.917 

41.726 

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1930.919 

155.771 

43.941 

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148.179 

41.800 

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1937.316 

156.033 

44.015 

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1753.455 

148.441 

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156.295 

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148.702 

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156.556 

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148.964 

42.021 

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1956.969 

156.818 

44.237 

50. 

1963.500 

157.080 

44.311 

16 


CIRCUMFERENCES  OF   CIRCLES   IN 


CIRCUMFERENCES   OF  CIRCLES, 
FROM   1    INCH  TO   20  FEET, 

Advancing'  by  an  eighth  of  an  inch. 


Circe 


Dinm.       ;    Circum. 


Diar 


1    3 


o 

:: 


1    7 
1 


1 


1     9f 

1  9i 
1  10 

1  101 
1  10J 

1  10| 
1  10| 

1  10| 

i  io| 
1  11 
1  HI 

1  Hi 
1  111 

1  111 


FEET,   INCHES,   AND    EIGHTHS. 


17 


6     9J 


Diam. 


84 


3     0- 


8    5fr 
8    6 


3     64 


10    21 


3    9| 


I/MUU.     L/ircuin. 

FT. 

IN. 

FT.   IK. 

3 

10 

12  04 

3 

104, 

12  05 

3 

101 

12  V. 

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12  l| 

3 

lOi 

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3 

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18          CIRCUMFERENCES  OF  CIRCLES  IN 

Diam.  .  Circum.    Diam.    Circum.    Diam.    Circum.    Diam. 

|  Circum. 

FT.  IN. 

FT.  IN. 

FT.  IN. 

FT.  IN. 

FT.   IN. 

FT.   IN. 

FT.  IN. 

!   FT.    IN. 

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FEET,  INCHES,    AND    EIGHTHS. 


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Circum. 


26  8f 
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27  Oi 

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20 


CIRCUMFERENCES  OF   CIRCLES    IN 


Circum. 

Diam. 

Circum. 

Diam. 

Circum. 

Diam. 

Circum. 

FT.   IN. 

FT.  IN. 

FT.   IN. 

FT.   IN. 

FT.   IN. 

FT.   IN. 

1  FT.   IN. 

28   6| 

9  8 

30  4| 

10  3 

32  2§ 

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22 

Diam. 

C 

Circum. 

[RCUMFERENCES 

Diam.   |  Circum. 

OF  CIRCLES  I 

Diam.   i  Circum. 

M 
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FEET,  INCHES,   AND    EIGHTHS. 


23 


Diam. 

Circum. 

Diam. 

Circum. 

Diam. 

Circum. 

Diam. 

Circum. 

T.   IN. 

FT.   IN. 

FT.   IN. 

FT.   IN. 

FT.   IN. 

FT.   IN. 

FT.  IN. 

FT.   IN 

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24 


CIRCUMFERENCES  OF  CIRCLES. 


Diam.  Circum. 


Circum. 


18    8 


19  2^ 
19  2 


"s 

3 


59  81 
59  8f 
59  9 
59  9f 
W»  9f 
59  101 
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59  11 
59  llf 

59  llf 
CO  0| 

60  01 


19     41 


19 


7J 


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62  2J 
62  2£ 
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63  01 
63  0| 


AREAS   AND    CIRCUMFERENCES    OF    CIRCLES.  25 


APPLICATION   OF   THE    PRECEDING   TABLE  (P.  5-9). 

EXAMPLE  1. — What  is  the  area  of  a  circle  10  feet  6  inches  in  di- 
ameter ? 

At  page  5,  in  column  8,  and  opposite  to  10J,  is  86.590,  which  is 
the  result  required. 

EXAMPLE  2. — What  is  the  circumference  of  a  circle  10^  inches  in 
diameter  ? 

At  page  5,  in -column  9,  and  opposite  to  10£,  is  32.99,  which  is  the 
result  required. 

When  it  is  required  to  reduce  the  decimal  remainders  in  this  table  to  de- 
nominations of  yards,  feet,  inches,  etc, 

Multiply  the  decimal  by  the  number  of  parts  in  the  denomination 
required,  and  cut  off  as  many  places  for  a  remainder,  to  the  right 
hand,  as  there  are  places  in  the  given  decimal.  '.+  -. ' 

EXAMPLE. — What  is  the  value  of  .590  foot  ? 
.590 
12  inches  in  a  foot. 


>  .   7.080 
7  inches  and  .080  of  an  inch. 


APPLICATION   OP   THE   PRECEDING   TABLE  (P.  16-24). 

In  addition  to  the  general  use  of  this  table  in  giving  the  circum- 
ferences of  circles  from  one  inch  to  twenty  feet  in  diameter,  in  the 
ordinary  designations  of  feet,  inches,  and  eighths,  it  is  of  especial 
utility  in  its  adaptation  to  the  requirements  of  boiler-makers  and 
blacksmiths  in  the  determination  of  the  length  of  materials  required 
for  hoops,  tyers,  etc.,  etc. 

Rote. — In  the  formation  of  metallic  hoops,  tyers,  etc.,  a  contraction  of  their  in- 
ner surface  takes  place,  the  exact  allowance  for  which  is  the  thickness  of  the 
metal,  which,  therefore,  must  be  added  to  the  diameter  for  which  the  circumfer- 
ence is  required. 

EXAMPLE. — What  is  the  length  of  a  bar  required  to  form  a  hoop 
of  6  feet  9^  inches  in  diameter,  the  thickness  of  the  metal  being  \ 
an  inch? 

6  feet  9£  inches,  added  to  \  an  inch,  gives  6  feet  9|  inches  for  the 
diameter,  the  circumference  for  which  (page  19)  is  21  feet  4$  inch- 
es, which  is  the  result  required. 

Note. — When,  in  the  formation  of  hands,  etc.,  the  bar  of  metal  is  to  be  bent 
upon,  its  edge,  the  breadth  of  the  bar  must  be  added  to  the  diameter,  instead  of 
the  thickness  of  it. 

B 


26  CIRCUMFERENCES    OF    CIRCLES. 

When  a  flanged  or  ribbed  bar  is  used,  as  with  rail-car  tyers, 
tanks,  etc. 

The  contraction  of  the  inner  surface  of  the  metal  and  the  neces- 
sary addition  to  the  diameter  of  the  wheel  or  hoop  will  depend  upon 
the  conformation  of  the  bar,  inasmuch  as  the  weakest  edges  will  both 
contract  or  attenuate  the  most,  according  as  they  are  upon  the  inner 
or  outer  surface. 

When  the  tyer  or  bar  has  its  flange,  on  the  outside. 

To  the  inner  diameter  add  the  thickness  of  the  metal  and  two 
thirds  of  the  breadth  of  the  flange. 

Application  of  the  preceding  table  to  an  elliptic  hoop. 

To  half  the  sum  of  the  diameters  add  the  thickness  of  the  metal, 
and  proceed  as  directed  for  plain  bars. 

In  the  construction  of  elliptic  hoops  of  angled  iron,  reference  must 
be  had  to  the  tables  for  angled  iron :  thus,  when  the  angle  is  out- 
side, it  must  be  added  to  the  diameter,  and  when  it  is  on  the  inside, 
it  must  be  subtracted  therefrom. 

NOTE. — In  determining  the  length  of  a  bar,  an  allowance  for  the 
thickening  of  the  ends  must  be  made  where  welding  is  necessary. 

Mr.  James  Foden,  of  Liverpool,  has  found  that,  in  an  angled  bar  of  uniform 
thickness,  the  curve  that  will  exactly  compensate  for  the  greater  contraction  of 
its  inner  surface,  when  it  is  bent  in  a  ring,  is  one  of  which  four  times  the  circum- 
ference of  the  ring  is  its  radius. 

Application  of  the  table  to  the  construction  of  teethed  wheels. 

To  ascertain  the  circumference  and  diameter  of  a  wheel,  for  a  given  num- 
ber of  teeth  and  pitch. 

RULE. — Multiply  the  pitch  of  the  teeth  by  the  number  of  teeth  the 
wheel  is  to  contain,  and  the  product  will  be  the  circumference. 

EXAMPLE. — The  pitch  of  a  tooth  is  to  be  2£  inches,  and  the  num- 
ber of  teeth  60 ;  what  will  be  the  circumference  and  diameter  of 
the  wheel  ? 

60    number  of  teeth. 
2|-  pitch. 
120" 
30 
7j 
12)157* 

13  H  circumference  of  wheel. 

In  column  8,  page  17,  opposite  to  this,  is  4  feet  2£  inches,  which  is 
the  diameter  required. 

NOTE. — In  the  construction  of  these  tables,  where  the  last  fraction  has  been 
equal  to  or  exceeded  .5,  1  has  been  added.  Thus,  3.14159,  if  set  down  to  four 
places  of  decimals,  would  be  3.1416. 


CIRCUMFERENCES    OF    AKGLED   HOOPS. 


27 


CIRCUMFERENCES  OF  ANGLED   HOOPS, 
From  6  inches  to  10  feet. 

ANGLED    OUTSIDE. 


Fig.  1. 


NOTE.— The  breadth  of  the  edge  flange  (2 })  must  be  added  to  the  inner  diameter 
(10)  of  the  hoop  or  ring  required. 


INCH. 

6. 


10. 


FT.      IN, 
1        &3 

1    6 

II 


10* 

lOf 

St 

1 11 
1 11 

2 

2 

2  0 

2  1 

2  1 

2  2 

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2 

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2  3 

2  41 

2  4 

2  5 

2  51 

2  5| 

2  6 
2 
2 
2 
2 

2  74 


2    1 


28 


CIRCUMFERENCES   OF    ANGLED    HOOPS. 


Diam 

Circum. 

Diam. 

Circum. 

Dinm. 

Circum. 

Diam. 

Circum. 

FT.   I> 

FT.   IN. 

FT.   IN 

FT.   IN. 

FT.   IN. 

FT.  JN. 

FT.  IN. 

FT.   JN. 

2  2 

6  41 

2  9 

8  Of 

3  4 

9  91 

3  11 

11  5f 

2  2- 

r 

6  4| 

2  9^ 

I 

8  It 

3  4£ 

9  9f 

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11  6i 

2  2: 

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2  9, 

f 

8  l| 

3  41 

9  10 

3  Hi 

11  e| 

2   2; 

! 

6  51 

2  9 

8  if 

3  4| 

9  lOf 

3  ll| 

11  6| 

2  2- 

6  5| 

2  9- 

, 

8  2i 

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9  lOf 

3  111 

11  71 

2  2 

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11  7f 

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i 

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r 

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7  11; 

3  3- 

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CIRCUMFERENCES    OF    ANGLED    HOOPS. 


29 


Dism.      !    Circ 


II 

19 

19 

19 

19  10]^ 

19  llf 

19  llf 

20 


30 


CIRCUMFERENCES    OF    ANGLED    HOOPS. 


Diam. 

Circnm. 

Diam. 

Circum. 

Diam. 

Circum. 

Diam. 

;  Circum. 

FT.  IN. 

FT.   IN. 

FT.  IN 

FT.   IN. 

FT.  IN. 

FT.   IN. 

FT.   IN. 

FT.   IN. 

6  10 

20  Of 

7  5 

' 

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8  01 

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23  61 

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8  71 

25  21 
25  2f 

6  10} 

20  14 

7  5] 

21  10 

8  of 

23  G| 

8  7f 

25  3 

6-101 

20  If 

7  5i 

21  lOf 

8  Oi 

23  6| 

8  71 

25  3f 

6  10* 

20  21 

7  5| 

21  lOf 

8  M 

23  7| 

8  7| 

25  3f 

6  lOf 

20  21 

7  5i 

21  114 

8  Of 

23  7| 

8  7| 

25  4| 

6  lOf 

20  2| 

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8  Of 

23  8 

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25  4| 

6  11 

20  31 

7  6 

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8  8 

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8  8£ 

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20  4 

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8  81 

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8  If 

23  9f 

8  8| 

25  6 

6  114 

20  4f 

7  6J 

22  li 

8  14 

23  9f 

8  84 

1  25  61 

6  llf 

20     63 

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9  If 
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Diam. 

CIR 

Circum. 

CUMFER 

Diam. 

ENCES  C 

Circum. 

>F  ANGI 

Diam. 

.ED  HOC 

Circum. 

)PS. 

Diam. 

3 

Circum. 

9  2 

26  lOf 
26  10| 

9  4i 

9  4| 

27   5f 

27  61 

9   7 

28  H 
28  l| 

9  9i 

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27  6| 

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28  9i 

9  2* 

26  ll| 

9  5 

27  7i 

9  1\ 

28  2i- 

9  10 

28  9| 

9  2| 

27  Oi 

9  51 

27  74 

9  7-| 

28  2} 

9  10^ 

28  101 

9  2f 

27  0| 

9  5i 

27  8 

9  7f 

28  31 

9  101 

28  lOf 

9  2| 

27  1 

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27  8f 

9  7| 

28  3| 

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28  11 

9  3 

27  If 

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9  8 

28  4 

9  10| 

28  11 

9  34 

27  If 

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27  9 

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28  4f 

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9  31 

27  2i 

9  5f 

27  9f 

9  8i 

28  4f 

9  lOf 

29  0 

9  3f 

27  21 

9  5| 

27  9f 

9  8| 

28  oj 

9  10| 

29  0 

9  31 

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27  101 

9  84 

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29  O; 

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28  6i 
28  6-f 

9  111 
9  ll| 

29  1 
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27  ll| 

9  9 

28  7 

9  1H 

29  2 

9  4^ 

27  4-f 

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28 

9  '9| 

28  7f 

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29  2 

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9  6f 

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28  Of 
28  Of 

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28  7f 
28  8 

9  111 
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29  3 
29  3{ 

EXAMPLE.  —  The  inner  diameter  of  a  hoop  of  2£  inches  angled  iron 
(fig.  1,  p.  27)  is  to  be  10  inches  ;  what  is  the  length  of  the  bar  re- 
quired ? 


=  12^,  and  the  circumference  for  this  (page  27)  is  3  feet 
and  f  ths  of  an  inch. 

The  preceding  table  is  calculated  upon  the  proportion  of  the  diam- 
eter of  a  ring  (of  angled  metal)  to  its  circumference,  being  as  1  to 
2.9312. 


32 


CIRCUMFERENCES    OF   ANGLED   HOOPS. 


CIRCUMFERENCES  OF  ANGLED   HOOPS, 
From  6  inches  to  10  feet. 

ANGLED    INSIDE. 


Fig. 


NOTE. The  breadth  of  the  inner  flange  must  be  taken  from  the  outer  diameter 

of  the  ring  or  hoop  required. 

Cireunu    «•     Diam.      i     Cirenm. 


7. 


8. 


9. 


2    3 


3    5 


81 


10 
101 

101 


1  10 


1 11 

i  lit 

1  111 
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1  111 
1  llf 

ml 

2 

2  04 
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2  li 


5  111 

6  03 
6  Of 

6  1-1 

6  2 

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G  8£ 
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7  Of 
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7  li 

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7  4| 


CIRCUMFERENCES  OF    ANGLED    HOOPS. 


CIRCUMFERENCES    OF   ANGLED   HOOPS. 


Diarn. 

Circum. 

Diam. 

Circum. 

Diam.    Circum. 

Diam.    Cinroro, 

IT,  IN. 

FT.   IN. 

FT.  IN. 

PT.   IN. 

FT.  IN. 

FT.   IN. 

FT.  IN. 

FT.   IN, 

4  6 

15  5 

5  1 

17  4f 

5  8 

19   4| 

6  3 

21  4| 

4  6£ 

15  5f 

5  1| 

17  54 

5  8^ 

19  5| 

6  31 

21  oi 

4  6i- 

15  5f 

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CIRCUMFERENCES    OF   AKGLED    HOOPS. 


35 


Diam. 

Circum. 

Diam. 

Circum. 

Diam. 

Ciicum. 

Diam. 

Circum. 

FT.  IN. 

FT.   IN. 

FT.  IN. 

FT.   IN. 

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86 


CIRCUMFERENCES    OF   ANGLED    HOOPS. 


Circum. 


Diam. 


9     6| 


FT.     IN 

9    7 
9    7* 
9 
'9 

S> 
9 


32    9| 


33     6" 


EXAMPLE. — The  outer  diameter  of  a  hoop  of  2^  inch  angled  iron 
(tig.  2,  p.  32)  is  to  be  12^  inches  ;  what  is  the  required  length  of  the 
hoop? 

12^  —  2^  =  10,  and  the  circumference  for  this  (page  32)  is  2  feet 
10£  inches. 

The  preceding  table  is  calculated  upon  the  proportion  of  the  diam- 
eter of  a  ring  (of  angled  metal)  to  its  circumference,  being  as  1  to 
3.4248. 


CUTTING    OF   BOILER   PLATES,  ETC. 


37 


CUTTING  OF  BOILER  PLATES,  MATERIALS  FOR  ROOF- 
ING, AND  THE  COVERING  OF  SOLIDS. 


Under  this  head  it  is  thought  necessary  to  illustrate  only  such  of  the  cases 
as  occur  in  general  practice. 

1.  To  ascertain  the  covering  for  a  cone,  A  B  C,fig.  1. 
d 


From  B  as  a  centre,  with  the 
radius  B  C,  describe  the  arc  of 
a  circle  C  d ;  make  C  d  equal  in 
length  to  the  circumference  of 
the  base  of  the  cone  (which  can 
be  found  by  a  reference  to  the 
table  of  the  circumferences  of  a 
circle)  and  join  B  d ;  then  the 
figure  determined  by  B  d  C  will 
be  that  of  the  required  surface  of 
the  cone. 


2.  To  ascertain  the  surface  of  an  envelope  for  a  frustum  of  a  cone, 

.  2. 


Produce  A  C,  B  D,  until  they 
meet  at  E  ;  then  from  E  as  a  cen- 
tre, with  the  radii  E  A  and  E  C, 
describe  the  arcs  B  f  and  D  g, 
and  set  off  D  g  equal  to  the  cir- 
cumference of  the  base  of  the 
cone,  and  join  E  g ;  then  the  fig- 
ure B  D  f  g,  will  be  that  of  the 
required  surface  of  the  frustum. 


38 


CUTTING   OP   BOILER   PLATES,   COVERING 


3.  To  ascertain  the  surface  of  an  envelope  for  a  given  cylinder, 

/*    O. 


Let  A  B  C  D  be  the  given  cylinder,  having  one  of  its  ends  at  an 
angle  to  its  sides,  as  A  B. 

Upon  the  base  C  D  draw  a  semicircle,  which  divide  into  a  num- 
ber of  equal  parts  (the  more  there  are  the  more  correct  will  be  the 
result  required),  as  1,  2,  3,  4,  5,  and  6 ;  from  the  points  draw  the 
lines  1  1,  2  2,  3  3,  &c,,  parallel  to  the  plane  of  the  cylinder;  then 
set  off,  as  in  Jig.  4,  the  line  E  F  G,  equal  in  length  to  the  circumfer- 


« 

" 

I 

' 

iS 

^ 

^ 

i 

-  —  • 

I 

i 

i 

•• 

1 

1 

E 


3       2 


G 


ence  of  the  base  of  the  cylinder,  or  twice  the  semicircle  C  o  D; 
upon  E  F  G  mark  off  on  each  side  of  F  the  same  number  of  equal 
distances  as  in  the  semicircle  C  o  D,  and  draw  lines,  as  F  h,  1  1,22, 
3  3,  &c.,  perpendicular  to  E  F  G  ;  make  F  h  equal  in  length  to  A  C, 
and  E  i,  G  k,  each  equal  to  D  B,  and  also  each  of  the  perpendicu- 
lars equal  to  the  lines  bearing  the  same  figures,  as  1  1,  2  2,  3  3,  &c. ; 
then  a  line  traced  through  these  points  will  form  a  side  of , the  en- 
velope, the  whole  of  which  is  contained  in  the  figure  E  i  k  G. 

NOTE. — This  problem  is  a  very  useful  one  to  boiler-makers  and  coppersmiths 
who  are  in  the  habit  of  making  pipes  to  join  each  other  at  any  given  angle — the 
shape  of  the  plate  of  metal  for  making  which  will  be  readily  found  by  the  fore- 
going rule. 


TO   DOMES,  AND   VARIOUS   FIGURES.  39 

COVERING   OF   CIRCULAR   ROOFS,  ETC. 

Circular  roofs  may  be  covered  upon  two  different  principles  : 

First  Method. — Assume  the  vertical  section  or  axis  to  be  divided 
into  a  number  of  small  equal  parts,  and  the  roof  or  figure  cut  by 
planes  through  the  points  of  division  parallel  to  the  base,  and  then 
consider  the  portions  of  the  figure  as  so  many  frustums  of  cones ;  the 
surface  of  each  frustum  can  then  be  determined  as  by  rule  2,  p.  37. 

Second  Method. — Divide  the  circumference  of  the  base  into  a  num- 
ber of  small  equal  parts,  and  assume  sections  to  be  made  perpendic- 
ularly through  these  points  of  division ;  then  estimate  the  surface 
of  each  of  these  divisions  on  the  surface  of  the  figure. 

4.  To  cover  a  dome  by  the  first  method. 
Let  F  A  H,  fi<j.  5,  be  the  section  of  a  dome ;  draw  the  axis  o  A 

5  i 


produced  to  i ;  divide  the  curve  of  one  half  the  figure  into  equal 
parts,  as  b,  d,  f,  and  h ;  the  width  of  these  divisions  being  the  width 
required  by  that  of  the  material  with  which  the  dome  is  to  be  cov- 
ered. 


40 


CUTTING   OF   BOILER   PLATES,   COVERING 


Produce  H  h,  h  f,  f  d,  d  b,  and  b  A  severally,  until  they  intersect 
the  axis  o  A  i ;  then  (for  example),  from  the  point  1,  with  the  radii 
1  f  and  1  d,  describe  the  curves  f  m,  d  n ;  then  set  off,  as  by  rule  2, 
the  length  of  f  m  equal  to  the  circumference  of  the  base"  f  e,  and 
d  f  m  n  will  be  the  form  of  the  course  to  cover  that  of  d  c  e  f. 

In  the  same  manner,  the  form  of  the  coverings  for  the  other  por- 
tions can  be  found. 

It  will  be  observed  that  the  finding  of  the  centres  for  the  curves 
of  the  lower  courses  of  a  dome  of  large  diameter  will  be  inconvenient 
from  the  distances  being  frequently  inaccessible  with  ordinary  means. 

The  method,  therefore,  of  finding  these  distances,  when  they  are 
inconveniently  accessible,  is  as  follows : 

Let  ABC,  Jig.  6,  be  the  vertical  section  of  a  dome,  and  suppose 


6 


d  f  to  be  the  last  course  attained  by  construction  according  to  the 
preceding  rule,  draw  the  axis  o  B,  and  produce  it  and  f  d  to  meet 
in  P ;  from  the  centre  P,  with  the  distance  P  d,  describe  the  arc  d  1 ; 
join  d  1,  and  produce  the  line  to  m  on  the  curve  A  B ;  at  m,  draw 
m  f  and  m  h,  and  mark  the  points  of  their  intersection  of  o  B  by  t 
u ;  draw  f  p  and  h  r  parallel  to  A  C,  then  will  f  1  be  half  the  length, 
1  t  the  height  or  versed  sine  of  the  first  course,  and  h  r  the  half  length, 
and  r  u  the  height  or  versed  sine  of  the  remaining  course. 

NOTE. — The  height  or  versed  sine  corresponding  to  a  given  length  of  any  of 
these  courses,  is  found  as  shown  in  problem  9,  page  45. 


5.  To  cover  a  dome  by  the  second  method,  fig.  7. 

Let  ABC,  fig.  7,  be  the  section  of  a  dome ;  then  the  length  of  a 
course  of  covering  is  obtained  as  follows :  the  length  of  the  course 
C  e  is  equal  to  the  curve  A  C,  and  k  f  the  breadth  of  it ;  join  f  h, 
and  the  lines  1,  2,  3,  and  4  intersected  thereby  will  be  the  half 


TO  DOMES,   AND   VARIOUS    FIGURES. 


41 


breadths  (for  the  vertical  C  h)  of  the  course  at  the  corresponding 
lines  on  C  e,  through  which  points  a -line  can  be  drawn,  which  will 
give  the  form  of  the  course  required,  as  e  k  f . 


A 


6.  To  ascertain  the  outline  of  a  course  of  covering  to  a  dome 
without  reference  to  a  section  of  the  dome,  fig.  8  (p.  42). 

Let  A  B  be  the  breadth  of  the  course ;  bisect  it  at  c  by  the  per- 
pendicular d  f;  make  c  f  equal  to  the  length  of  the  arc  from  the 
base  of  the  dome  to  the  top  of  it  (which  may  be  found  either  by 
measurement  or  calculation)  ;  divide  the  semicircle  A  d  B  into  any 
number  of  equal  parts,  and  draw  the  sines  parallel  to  A  B ;  divide 
c  f  into  the  same  number  of  equal  parts,  and  draw  lines  parallel  to 
A  B  ;  make  ordinates  on  each  side  of  c  f,  as  1,  2,  and  3,  equal  to  the 
sines  of  A  d  B,  and  a  curve  drawn  through  their  terminations,  1,  2, 
and  3,  on  both  sides,  will  give  the  outline  of  the  course. 


42  CUTTING   OF  BOILER   PLATES,  COVERING 


7.  To  ascertain  by  calculation  the  breadths  of  the  courses  of 
covering  to  a  dome  when  in  vertical  sections  and  of  a  given 
or  required  width,  fig.  9. 


Let  A  B  C  be  the  vertical  section  of  a  dome,  and  the  required 
width  of  the  courses  to  be  -^th  of  the  circumference  of  the  base. 

Bisect  A  B  in  e,  and  erect  a  perpendicular,  e  C ;  divide  the  arc 
B  C  into  a  number  of  equal  parts  (six),  and  from  the  points  1,  2, 
3,  &c.,  draw  lines  parallel  to  A  B  ;  and  as  the  breadth  of  the  courses 


TO    DOMES,   AND    VARIOUS    FIGURES. 


43 


at  A  B  is  to  be  ^th  of  the  circumference  thereof,  it  follows  that  the 
breadth  at  1  1,  2  2,  &c.,  will  also  be  -^th  of  the  circumference  at 
these  points ;  the  diameter  then  being  ascertained  at  these  points, 
the  operation  is  as  follows : 

Assume  A  B  to  be  12  feet  in  diameter, 

and  that  5  5  is  by  measurement  11.6 

44"  "  10.4 

33"  "  8.5 

22"  "  6. 

and  11"  "  3.1 

Then  the  circumference  at  A  B  will  be  12x3.1416,  or  37.6992; 
hence,  the  breadth  of  a  course  at  that  line  will  be  37.6992-^24,  or 
1.57  feet.  The  circumference  at  5  5  will  be  11.6  x  3.146,  or  36.446, 
and  the  breadth  of  the  course  at  the  line  will  be  36.446-^-24,  or  1.52 
feet. 

In  like  manner,  the  circumference  at  4  4,  3  3,  2  2,  1  1,  will  be 
32.673,  26.704,  18.850,  and  9.739,  and  the  breadth  of  the  curves 
respectively,  1.36  and  1.11  feet,  .785  and  .405  inches. 


F       i      H 

Draw  F  H,  fig.  10,  equal  to  -^th  of  the  circumference  of  A  B 
(fig.  9) ;  bisect  it  at  i  by  a  perpendicular  line  i  K,  and  set  off  thereon 
six  equal  distances,  5,  4,  3,  2,  and  1,  the  same  as  upon  the  dome, 
and  make  the  breadths  at  these  points  equal  to  those  found  by  cal- 
culation ;  then  a  line  drawn  through  the  points  will  have  the  outside 
of  the  course  required. 


44  CUTTING    OF   BOILER   PLATES,   COVERING 


APPLICATION  OF  THE  PRECEDING  RULES  TO  THE 
SHELLS  OF  CYLINDRICAL  BOILERS  AND  FLUES. 

The  courses  of  a  cylindrical  boiler  or  flue,  when  tapered,  are  a 
series  of  conic  frustums  inserted  into  each  other,  the  height  of  each 
being  the  breadth  of  the  plate  of  the  course ;  the  diameters  at  the 
large  and  small  ends  being  respectively  equal  to  those  of  the  exter- 
nal and  internal  diameters  of  the  boiler  or  flue. 

9.  To  ascertain  how  to  cut  a  template  for  the  tapering  courses 
of  a  boiler  or  flue. 

Suppose  it  is  required  to  build  a  cylindrical  boiler  5  feet  in  diam- 
eter, the  shell  of  which  is  to  be  made  in  four  plates  of  equal  length, 
of  a  breadth  of  22  inches,  and  f  ths  of  an  inch  thick. 

NOTE. — In  referring  to  the  length  or  breadth  of  a  boiler,  or  any  riveted  plate, 
the  measurements  are  taken  an.l  given  from  the  centre  of  the  rivet  holes. 

The  first  operation  is  to  find  the  vertex  of  the  cone  of  which  the 
course  is  a  frustum,  the  rule  for  which  is  as  follows : 

Multiply  the  breadth  of  the  course  by  half  the  diameter  of  the 
boiler;  divide  their  product  by  the  thickness  of  the  metal,  and  the 
quotient  will  be  the  length  of  the  slant  edge  of  the  course. 

in.      in. 
Thus,  as  £  (.375)  :  30 : :  22  :  slant  edge  of  cone 

30 
.375)660 

1760  inches. 

Now  as  the  radius  with  which  the  template  is  to  be  drawn  is  of  an 
inconvenient  or  impracticable  length,  the  best  method  to  find  the 
curve  is  to  find  the  versed  sine  corresponding  to  the  curve,  for  which 
proceed  as  follows  : 

In  order  to  delineate  the  necessary  diagram,  Jig.  1 1 ,  first  obtain 
the  following  elements,  viz.,  the  radius  E  B,  the  distances  B  D  and 
A  B,  and  which  are  thus  found : 

E  B,  as  above  shown,  is  1760  inches,  B  D  is  the  fourth  of  the  cir- 
cumference of  the  shell,  which  is  to  consist  of  four  plates,  like  to 
A  C  D  B ;  consequently,  B  g  is  one  half  of  one  fourth  of  the  circum- 
ference of  the  shell;  thus,  the  diameter  of  the'boilers  being  5  feet, 
the  circumference  is  188.5  inches;  then  188.5-f-4=47.12,  and  47.12 
-H2  =  23.56  inches;  A  o  being  equal  to  the  width  of  the  course,  it 
is,  as  here  given,  22  inches. 


TO    DOMES,    AND    VA1UOUS    FIGURES. 


45 


E  B  is  the  radius,  B  D  the  chord,  and  g  H  the  versed  sine  of  the 
arc  first  required.  (See  Note,  page  40.)  The  rule  to  obtain  which 
is,  from  the  square  of  the  radius  (E  B)  subtract  the  square  of  half 
the  chord  of  the  arc  (g  B),  and  the  square  root  of  the  remainder 
subtracted  from  the  radius  will  give  the  versed  sine  (g  H). 

ILLUSTRATION.— The  radius  is  1760,  and  half  the  chord  of  the  arc 
is  23.56  inches. 

Then     1760  23.56 

1760  23.56 


3097600 =E  B3  555.0736 =g  B3 

555.0736 

3097044.9264,  the  square  root  of  which  is  1759.84 
=E  g,  and  1759.84  subtracted  from  1760=. 16=g  H  the  versed  sine. 


46 


CUTTING   OF   BOILER   PLATES,   COVERING 


Draw  upon  a  plate,  fig.  12  (from  which  a  template  is  to  be  made), 
a  straight  line  as  B  D=47.12  inches ;  bisect  it  by  A  E,  and  set  off 
g  A,  the  versed  sine  =  .16  inch;  then,  by  bending  a  batten  around 
the  points  BAD,  the  curve  of  the  outside  edge  of  the  course  may 
be  readily  drawn. 


B.-,, 


As  the  diameter  of  the  small  end  of  the  required  frustum  is  twice 
the  thickness  of  the  plate  less  than  the  larger,  or  (60  — f  x2)  59£ 
inches,  the  circumference  will  be  59£  X  3.1416  =  186.14  ;  hence  the 
length  of  the  plate  on  the  inside  will  be  186. 14-=-4= 46.53  inches. 
The  distance  between  the  rivet  holes  is  to  be  about  2  inches,  conse- 
quently the  templates  will  contain  23  divisions  in  the  length  and 
11  in  the  breadth.  The  template  can  now  be  drawn,  and  will  be  as 
shown  in  Jig.  13,  viz.,  a  b= 46.53  inches,  c  d=47.12  inches,  and  e  i 
=22  inches. 

13 


When  the  flue  is  of  the  form  of  the  following  figure. 

Assume  a  b,  c  d,  each  =  12  inches  in  length,  a  c=9  inches  in  diam- 
eter, and  that  a  course  is  to  be  18  inches  wide  and  i  of  an  inch  in 
thickness ;  distance  between  the  rivet  holes  2  inches. 


14 


i> 

D 


TO   DOMES,  AND    VARIOUS    FIGURES.  47 

in.  .  in.      in. 

: :  18  :  slant  of  edge  of  cone,  or  radius  of  circle  of 
4i  the  outer  edge  of  the  template. 

72~ 
_9 

"324  inches. 

The  diameter  of  the  semicircular  ends  be- 
ing 9  inches,  the  circumference  of  each  part 
will  be  9x3.1416-^-2  =  28.2744-^2  =  14.13 
inches  for  the  larger  end,  and  for  the  versed 
sine  proceed  as  before  shown.  324  being 
the  radius  of  the  arc,  and  14.13-f-2=7.06 
half  the  chord  of  the  arc ;  therefore, 
324  7.06 

324  7.06 


c2,  49.8436=c  i3, 

and  104976  -  49.8436  =  104926.2,  the  square 
root  of  which  is  323.9,  which,  when  subtract- 
ed from  324,  gives  ,l=f  i,  the  versed  sine 
of  arc  c  fd  of  outer  edge  of  template,^.  15. 
The  diameter  of  the  small  side  of  the 
semicircular  ends  will  be  (9  — ix2)  8£ 
inches,  consequently,  the  circumference  of 
8£x3.1416=26.70 

2  :     2 

inches. 


each    will   be 


=  13.35 


NOTE. — In  these  examples  it  will  be  perceived 
that  the  length  of  the  chord  is  measured  upon  the 
plate  from  the  length  of  the  curve  of  the  arc ;  this 
is  not  strictly  correct,  as  the  chord  is  shorter  than 
the  arc ;  this  difference,  however,  is  so  little  in  or- 
dinary cases,  that  is,  the  example,  p.  45,  being  but 
.16  of  an  inch,  that  it  was  considered  an  unnecessary 
element  to  bring  into  the  calculation  for  ordinary 
practice,  inasmuch  as  it  involves  a  complexity  at 
variance  with  the  purpose  of  these  rules.  In  cases, 
however,  requiring  exactness  of  dimension,  the 
manner  of  proceeding  is  as  follows : 

To  find  the  chord  of  the  arc. 

Multiply  the  versed  sine  by  2,  and  subtract  the  product  from  the  diameter; 
then  subtract  the  square  of  the  remainder  from  the  square  of  the  diameter,  and 
the  square  root  of  the  remainder  will  give  the  chord  required. 


WEIGHT    OF    SQUARE    ROLLED   IRON. 


WROUGHT  IRON. 

WROUGHT  IRON  expands  14^o00  of  its  length  for  one  degree  of 
heat;  will  bear  on  a  square  inch,  without  permanent  alteration, 
17,800  Ibs.,  and  an  extension  in  length  of  j^Vo  5  its  cohesive  force 
is  diminished  3^7  by  an  increase  of  1  degree  of  heat. 


Compared  with  cast  iron,  its  strength  is  1.12  times,  its  extensibility 
0.86  times,  and  its  stiffness  1.3  times. 


WEIGHT  OF  SQUARE  ROLLED  IRON, 

From  -f^th  of  an  inch  to  12  inches  square. 
ONE    FOOT  IN   LENGTH. 


Size  in    I    Weight  in 
inches.    |      pounds. 

Size  in 
inches. 

Weight  in 
pounds. 

Size  in 
inches. 

Weight  in 
pounds. 

Size  in 
inches. 

Weight  in 
pounds. 

jjy 

.0132 

2.1 

19.063 

5.§ 

106.931 

8.f 

266.193 

.0528 

24 

21.122 

5't 

111.737 

9. 

273.744 

s. 

.1188 

2.| 

23.287 

5.1 

116.647 

9.i 

281.401 

i 

.2112 

2.1 

25.558 

6. 

121.164 

9.| 

289.163 

JL 

.3300 

2.  1 

27.934 

6.4 

126.786 

9.1 

297.031 

$ 

.4753 

3. 

30.416 

6.- 

132.014 

9.1 

305.004 

is5> 

.6469 

3.4 

33.003 

6. 

137.347 

9.1 

313.084 

i 

.8449 

3-i 

35.697 

6. 

142.786 

9.f 

321.269 

1.069 

3.  1 

38.495 

6. 

148.331 

9.1 

329.559 

1.320 
1.597 

3.i 

3.| 

41.400 
44.410 

8.1 

e.j 

153.981 
159.737 

10. 
10.1 

337.955 
346.457 

, 

1.901 

3-f 

47.525 

/  . 

165.598 

10.1 

355.064 

is 

2.231 

3.| 

50.746 

74 

171.565 

10.  | 

363.777 

1 

2.587 

4. 

54.073 

7-1 

177.638 

10.1 

372.597 

L| 

2.970 

4.J 

57.505 

7-1 

183.816 

10.|- 

381.520 

1. 

3.380 

41 

61.043 

7.1 

190.100 

10.  f 

390.550 

1.1 

4.277 

4.| 

64.687 

7.1 

196.489 

10.  1 

399.685 

1.1 

5.281 

4.1 

68.436 

7-f 

202.984 

11. 

408.926 

l.| 

6.389 

4.1 

72.291 

7.| 

209.585 

11.  i 

418.272 

1.1 

l«l 

7.604 
8.924 

t:t 

76.251 
80.317 

8. 
8.1 

216.291 
223.103 

11.1 
11.1 

427.725 
437.282 

l.f 

10.350 

5. 

84.489 

8.1 

230.021 

11.1 

446.946 

1. 

11.881 

54 

88.766 

8.  f 

237.044 

11.  1 

456.715 

2. 

13.518 

5  i 

93.149 

8.1 

244.173 

11.1 

466.589 

2  1 

15  262 

5.1 

97.637 

8.| 

251.407 

11.  1 

476.570 

y 

17.109 

4 

102.232 

8.f 

258.747 

12. 

486.656 

WEIGHT   OF   WROUGHT   IRON    SHAFTING. 


49 


WEIGHT  OF  ROUND  ROLLED  IRON  AND  SHAFTING, 

From  ^th  of  an  inch  to  30  inches  diameter. 


ONE   FOOT   IN   LENGTH. 


Diameter 
iu  inches. 

Weight  in 
pounds. 

Diameter 
in  inches. 

Weight  in 
pounds. 

Dianwter 
in  inches. 

Weight  is 
pounds. 

TS 

.0104 

4.J 

50.803 

9.f 

245.889 

£ 

.0415 

44 

53.748 

9.f 

252.317 

Tff 

.0933 

4.f 

56.775 

9.J 

258.828 

i 

.1659 

4.f 

59.886 

10. 

265.422 

i5 

.2592 

4,| 

63.079 

104 

272.190 

•f 

.3733 

5. 

66.355 

10.1 

278.859 

•JHJ 

.5080 

5.i 

69.715 

10.  § 

285.702 

1 

.6636 

5.'| 

73.157 

10.  ^ 

292.628 

ae 

.8398 

5.| 

76.682 

10.  | 

299.636 

1.037 

5.1 

80.290 

10.  f 

306.729 

li 

1.255 

**•* 

83.981 

10.  1 

313.904 

I 

1.493 
1.752 

5'f 

87.755 
91.612 

11. 

11.1 

321.162 

328.502 

•| 

2.032 

6. 

95.552 

11.1 

335.926 

^f 

2.333 

6.| 

99.575 

11.  1 

343.432 

1. 

2.654 

64 

103.681 

n.l 

351.022 

14 

3.359 

6.f 

107.869 

11.  | 

358.694 

1.1 

4.147 

64 

112.140 

ii.l 

366.449 

l.| 

5.028 

6.| 

116.505 

n.| 

374.288 

•       1.1 

1-1 

5.922 
7.009 

6"t 

120.943 
125.463 

12. 

12.1 

382.208 
390.212 

1-f 

8.129 

7. 

130.057 

12.1 

398.300 

l.f 

9.331 

74 

134.753 

12.  | 

406.470 

2. 

10.617 

7.1 

139.522 

12.1 

414.722 

24 

11.985 

7-f 

144.375 

12.  | 

423.059 

2-l 

13.437 
14.971 

7't 

149.300 
154.318 

12.  | 
12.  | 

431.477 
439.979 

1:1 

16.589 
18.259 
20.073 

p 

159.419 
164.603 
169.870 

13. 

134 
13.  | 

448.564 
457.232 
465.982 

24 

21.939 

84 

175.220 

13  2. 

474.816 

3. 

23.888 

8.1 

180.653 

134 

483.732 

34 

25.920 

8.1 

186.169 

13.| 

492.732 

3. 

28.035 

8.| 

191.767 

13.  f 

501.814 

3.^- 

30.233 

8.f 

197.449 

13.  | 

510.980 

3'. 
S.l 

3.| 

32.514 

34.878 
37.325 
39.855 

8.| 

9. 
94 

203.214 
209.061 
214.992 
221.005 

14. 

144 
14.1 
14.  | 

520.228 
529.559 
538.973 
548.470 

4. 

42.468. 

9.1 

227.102 

14.1 

558.050 

1! 

45.163 
47.942 

9.  jf 

233.281 
239.544 

14.  f 
14.  | 

567.713 
577.459 

50 


WEIGHT   OF   WROUGHT   IRON   SHAFTING. 


Diameter 
in  inches. 

Weight  in 
pounds. 

Diameter 
in  inches. 

Weight  in 
pounds. 

Diameter 
in  inches. 

Weight  in 
pounds. 

144 

587.288 

20. 

1061.689 

25.1 

1692.232 

15. 

597.200 

20.1 

1088.397 

25.} 

1725.908 

6171273 

20.} 

1115.437 

25.  f 

1759.915 

15  .*} 

637.677 

20.  1 

1142.809 

26. 

1794.254 

15.  | 

658.413 

21. 

1170.512 

26.1 

1828.925 

16. 

679.481 

21.1 

1198.547 

26.} 

1863.927 

16  i 

700.881 

21.} 

1226.915 

26.  f 

1899.262 

16.'* 

7221612 

21.  f 

1255.613 

27. 

1934.928 

16.  | 

744.675 

22. 

1284.644 

27.1 

1970.926 

17. 

767.070 

22.1 

1313.006 

27.} 

2007.256 

789.797 

22.} 

1343.700 

27.  | 

2043.917 

17  'I 

8121855 

22.  f 

1373.726 

28. 

2080.910 

17.  f 

836.246 

23. 

1404.083 

28.1 

2118.235 

18. 

859.968 

23.1 

1434.773 

28.1 

2155.892 

18.1 

884.022 

23.} 

1465.794 

28.  f 

2193.880 

18.} 

908.408 

23.  f 

1487.147 

29. 

2232.207 

18.  1 

933.125 

24. 

1528.832 

29.1 

2270.853 

19. 

958.174 

24.1 

1560.849 

29.1 

2309.837 

19.1 

983.555 

24.} 

1593.197 

29.  | 

2359.152 

1009  1268 

24.  1 

1625.877 

30. 

2388.800 

gj 

1035.313 

25. 

1658.889 

WEIGHT   OF   FLAT   ROLLED    IRON. 


51 


WEIGHT  OF  FLAT  ROLLED  LEON, 

From  i  X  J  Inch  to  5|  X  6  Inches, 

AND   ONE   FOOT   IN   LENGTH. 


Breadth 
in  inches. 

Thickness 
in  inches. 

Weight  in 
pounds. 

Breadth 
in  inches. 

Thickness 
in  inches. 

Weight  in 
pounds. 

Breadth 
n  inches. 

Thickness 
in  inches. 

Weight  in 
pounds. 

4 

0.211 

1-1 

0.580 

1-1 

M 

8.132 

0.482 

1.161 

1,1 

8.871 

0.634 

1.742 

!•! 

9.610 

•i 

•\ 

0.264 
0.528 

;: 

2.325 
2.904 

M 

'' 

0.792 
1.584 

0.792 

.• 

3.484 

,  ; 

2.376 

1.056 

rt 

4.065 

3.168 

•1 

'] 
*1 

.•i 

•1 

0.316 
0.633 
0.950 
1.265 
1.584 

14 

1:1 

4.646 

5.227 
5.808 
0.633 
1.266 
1.900 

T-(T-llH 

1 

3.960 
4.752 
5.544 
6.336 
7.129 
7.'921 

•1 

4 

0.369 

•  1 

2.535 

1 

8.713 

^i. 

0.738 

•  f 

3.168 

l^ 

9.505 

•8 

1.108 

t  8. 

3.802 

Jt 

10.297 

"1 

1.477 

i 

4.435 

i! 

11.089 

:| 

1.846 
2.217 

1. 

14 

5.069 
5.703 

2. 

0.845 
1.689 

i. 

0.422 

1.1 

6.337 

2.534 

0.845 

1-1 

6.970 

3  379 

1.267 

1.1 

0.686 

4.224 

1.690 

1.372 

5.069 

2.112 

J 

2.059 

m 

5.914 

2.534 

2.746 

6.758 

2.956 

t. 

3.432 

7.604 

14 

.. 

0.475 

.. 

4.119 

8.448 

.. 

0.950 

,! 

4.805 

9.294 

.• 

1.425 

1. 

5.492 

10.138 

.- 

1.901 

14 

6.178 

LI       10.983 

.. 

2.375 

1.1 

6.864 

l.f       11.828 

2.850 

1.1 

7.551 

l.|       12.673 

,. 

3.326 

1      i 

8.237 

24 

0  898 

i. 

3.802 

M 

4 

0.739 

••  8 

'. 

1.795 

i.j, 

0.528 

i 

1.479 

2.693 

1.056 

.. 

2.218 

,. 

3.591 

.. 

1.584 

.. 

2.957 

ij 

4.488 

.. 

2.112 

.. 

3.696 

,. 

5.386 

.. 

2.640 

,. 

4.435 

. 

6.283 

.• 

3.168 

5.178 

1. 

7.181 

.. 

3.696 

i!  . 

5.914 

14 

8.079 

i. 

4.224 

14 

6.653 

l.| 

8.977 

l.i       4.752 

14 

7.393 

1-1 

9.874 

52 


WEIGHT    OP    FLAT    ROLLED    IRON. 


Breadth 
in  inches. 

Thickness 
in  inches. 

Weight  in 
pounds. 

Breadth 
in  inches. 

Thickness 
in  inches. 

Weight  in 
pounds. 

Breadth 
in  inches. 

Thickness 
in  inches. 

Weight  in 
pounds. 

24 

1.1 

10.772 

24 

2. 

16.896 

24 

l.f       13.360 

1'f 

11.670 

2.- 

17.952 

1-1 

14.574 

l.f 

12.567 

2.^ 

19.008 

1-1 

15.789 

l.| 

13.465 

2. 

20.064 

l.f 

17.003 

2. 

14.362 

"   2.  f 

1.109 

1-1 

18.218 

24 

.950 

**•  a 

2.218 

2. 

19.432 

1.900 

3.327 

24 

20.  §47 

2.851 

4.436 

2-i 

21.861 

3.802 

5.545 

2.4 

23.076 

4.752 

6.654 

2.  1 

24.290 

5.703 

•  '"•  . 

- 

7.763 

2-1 

25.505 

6.653 

1!° 

8.872 

2-f 

26.719 

. 

7.604 

14 

9.981 

3. 

_1 

1.267 

i 

8.554 

i.l 

11.090 

! 

2.535 

"1 

9.505 

i.| 

12.199 

•  1 

3.802 

•8 

10.455 

i.l 

13.308 

_JL 

5.069 

1 

11.406 

i.l 

14.417 

•1 

6.337 

•f 

12.356 

i.f 

15.526 

•f 

7.604 

l.f 

13.307 

lit 

16.635 

•I 

8.871 

l.| 

14.257 

2. 

17.744 

1. 

10.138 

2. 

15.208 

2-1 

18.853 

},} 

11.406 

24 

16.158 

2.: 

19.962 

1   I 

12.673 

2.£ 

1.003 

2. 

21.071 

l-I 

13.940 

*"8 

2.006 

2. 

22.180 

1.1 

15.208 

3.009 

2.f 

1.162 

I.I 

16.475 

4.013 

* 

2.323 

L-i 

17.742 

5.016 

3.485 

14 

19.010 

;, 

6.019 

4.647 

2. 

20.277 

- 

7.022 

;i[ 

5.808 

24 

22.811 

1.'° 

8.025 

I 

6.970 

2.| 

25.346 

i'4 

9.028 

4 

8.132 

2.f 

27.881 

14 

10.032 

1. 

9.294 

3.i 

.1 

1.373 

t 

1.1 

11.035 

i.J 

10.455 

.i 

2.746 

14 

12.038 

i.j 

11.617 

.1 

4.119 

l.f 

13.042 

l. 

12.779 

.1 

5.492 

i.l 

14.045 

l. 

13.940 

.1 

6.865 

l.| 

15.048 

l.; 

15.102 

'-~M 

8.237 

2. 

16.051 

lJ 

16.264 

.1 

9.610 

2.J 

17.054 

iJ 

17.425 

1. 

10.983 

2.^ 

18.057 

2. 

18.587 

1-i 

12.356 

24 

1.056 
2.112 

24 
2-1 

19.749 
20.910 

1. 
1. 

,13.730 
15.102 

3.168 

2.1 

22.072 

I.I 

16.475 

4.224 

2.1 

23.234 

l.f 

17.848 

"; 

~ 

5.280 

2-1 

24.395 

l.f 

19.221 

*1 

6.336 

24 

1.215 

14 

20.594 

tl 

7.392 

8 

2.429 

2. 

21.967 

l'.8 

8.448 

'A 

3.644 

2.£       24.712 

9.504 

m. 

4.858 

2.| 

27.458 

10.560 

f. 

6.072 

2.f 

30.204 

J 

11.616 

,j 

7.287 

3. 

32.950 

12.672 

,. 

8.502 

34 

4 

1.479 

f. 

13.728 

1. 

9.716 

ti 

2.957 

.. 

14.784 

14 

10.931 

•1 

4.436 

,. 

15.840 

1-1 

12.145 

4 

5.914 

WEIGHT    OP    FLAT    ROLLED    IKON. 


Breadth   Thickness  Weight  in 
in  inches,    in  inches,      pounds. 

Breadth 
in  inches. 

Thickness 
in  inches. 

Weight  in 
pounds. 

Breadth 
in  inches. 

Thickness 
in  inches. 

Weight  in 
pounds. 

34 

«f 

7.393 

4-4 

4 

1.795 

5. 

1. 

16.897 

•f 

8.871 

,i 

3.591 

1.1 

21.122 

•1 

10.350 

4 

7.181 

I.i 

25.346 

1. 

11.828 

i 

10.772 

1.1 

29.570 

13.307 

1. 

14.364 

2. 

33.795 

14.785 

i.* 

17.953 

2.1 

38.019 

- 

16.264 

i.I 

21.544 

2.1 

42.243 

17.742 

i.I 

25.135 

2.1 

46.468 

19.221 

2. 

28.725 

8. 

50.692 

20.699 

2.1 

32.316 

3.1 

54.916 

22.178 

2.1 

35.907 

3.1 

59.140 

2. 

23.656 

2  \ 

39.497 

3-1 

63.365 

2.1 

26.613 

3. 

43.088 

4. 

67.589 

2.1 

29.570 

46.679 

4-i 

71.813 

2.1 

32.527 

50.269 

44 

76.038 

3. 

35.485 

53.860 

4.i 

80.262 

3.1 

38.441 

4.. 

57.450 

5.1 

4.436 

3.f 

4 

1.584 

44 

l 

3.802 

8.871 

.1 

3.168 

1 

7.604 

13.307 

-ir 

4.752 

.1 

11.406 

1. 

17.742 

4 

6.336 

1. 

15.208 

li 

22.178 

«!" 

7.921 

1.1 

19.010 

1.1 

26.613 

.£ 

9.505 

1-1 

22.812 

1.1 

31.049 

z 

11.089 

1.1 

26.614 

2. 

35.484 

i 

12.673 

2. 

30.415 

2.1 

39.920 

14 

14.257 

2.1 

34.217 

2.1 

44.355 

1.1 

15.841 

2-i 

38.019 

2.T 

48.791 

i.f 

17.425 

2.f 

41.820 

3. 

53.226 

i.I 

19.009 

3. 

45.623 

3.1 

57.662 

i.f 

20.594 

3-i 

49.425 

3.1. 

62.097 

i.j 

22.178 

3.$ 

53.226 

3.f 

66.533 

i. 

23.762 

B.I 

57.028 

4. 

70.968 

2. 

25.346 

4. 

60.830 

4.1 

75.404 

2.1 

28.514 

4.1 

64.632 

79.839 

24 

31.682 

4.f 

^ 

4.013 

4  f 

84.275 

Sfei 

34.851 

*T 

8.026 

5.'* 

88.710 

3. 

38.019 

•I 

12.039 

54 

4.647 

3.i 

41.187 

J£ 

16.052 

9.294 

34 

44.355 

i-i 

20.066 

13.940 

4. 

.i 

1.690 

14 

24.079 

'  1. 

18.587 

.1 

3.380 

i.i 

28.092 

I.i 

23.234 

.1 

6.759 

2. 

32.105 

1.1 

27.881 

1 

10.138 

2.1 

36.118 

1.} 

32.527 

1. 

13.518 

2.1 

40.131 

2. 

37.174 

1.1 

16.897 

2.1 

44.144 

2.1 

41.821 

p 

20.277 
23.656 

3. 

48.157 
52.170 

2.| 

46.468 
51.114 

2. 

27.036 

3.1 

56.184 

3'.* 

55.761 

2.1 

30.415 

3.1 

60.197 

3.1 

60.408 

24 

33.795 

4. 

64.210 

3.} 

65.055 

2.f 

37.174 

4.1 

68.223 

69.701 

3. 

40.554 

4.f 

72.235 

4]* 

74.348 

3.i 

43.933 

5. 

% 

4.224 

4.1 

78.995 

3.| 

47.313 

"j 

8  449 

4.|- 

83.642 

3.f 

50.692 

•I 

12.673! 

4-1 

88.288 

54 


WEIGHT    OF    FLAT    ROLLED    IRON. 


Breadth 
in  inches. 

Thickness 
in  inches. 

Weight  in 
pounds. 

Breadth 
in  inches. 

Thickness  Weight  in 
in  inches.      pounds. 

Breadth 
in  inches. 

Thickness 
in  inches. 

Weight  in 
pounds. 

54 

5. 

92.935 

5.f 

l.f      34.006 

5.| 

3.f 

72.870 

5.J 

97.582 

2.       ,38.864 

4. 

77.728 

5.f 

4.858 

2.J    !  43.722 

4-i 

82.585 

*f 

9.716 

2.1      48.580 

4.1 

87.443 

*1 

14.574 

2.1     I  53.437 

4*1 

92.301 

ll 

19.432 

3.         58.296 

5. 

97.159 

n 

24.290 
29.148 

3.i       63.154 
3.|     !  68.012 

a 

102.017 
106.876 

J 

6. 

116.592 

APPLICATION  OF  THE  PRECEDING  TABLES. 

The  dimensions  of  a  bolt  or  bar  of  iron  being  given,  find  its 
weight  in  the  appropriate  column,  which  is  for  the  length  of  one 
foot ;  multiply  this  weight  by  the  number  of  feet  and  parts  thereof 
in  the  bolt  or  bar,  and  the  product  is  the  weight. 

EXAMPLE  1. — What  is  the  weight  of  a  BAR  OF  SQUARE  IRON  !$• 
inches  square  and  6^  feet  in  length? 

Opposite  to  1£  inches  in  size,  in  table  at  page  48,  is  7.604  Ibs., 
which  is  the  weight  of  such  a  bar  for  a  length  of  one  foot. 
Hence  7.604  Ibs., 

multiplied  by       6£  feet, 

4562T 
3802 


is  equal  to       49.426  pounds. 

If  the  lesser  denomination  of  ounces  is  required,  the  result  is  obtained 
as  follows :  Multiply  the  remainder  by  16,  pointing  off  the  decimals 
as  in  multiplication  of  decimals,  and  the  figures  remaining  on  the 
left  of  the  point  indicate  the  number  of  ounces. 

Thus,  .426  of  a  Ib.  =  .426 
16 


6.816  ounces. 
The  weight,  then,  is  49  Ibs.  6  ounces  and  -fthfc- 

If  the  weight  for  less  than  afoot  in  length  was  required,  the  readiest 
operation  is  this : 

EXAMPLE  2. — What  is  the  weight  of  a  bar  or  bolt  6£  inches  square 
and  9f  inches  long  ? 

On  page  48,  column  5th,  opposite  to  6£,  is  132.040,  which  is  the 
weight  for  a  foot  in  length. 


WEIGHT   OF   HOUND   ROLLED   IRON.  55 

6jrXl2  inches ^132.040 

£     " is~T =  G6.020 
3.     "       is  i  of  6=  33.010 

.*  "       is  |  of  3=     5.5016  v 

.i  "       isiofj=     2.7508 
94  =107.2824,  or  107  pounds  and  -ffififc. 

EXAMPLE  3. — What  is  the  weight  of  a  BOLT  OR  ROD  or  IRON  2 
inches  in  diameter  and  9 f  feet  in  length  ? 

Opposite  to  2  inches  in  column  1st,  page  49,  is  10.617,  which  is 
the  weight  of  such  a  rod  for  the  length  of  one  foot. 
Hence  10.617  Ibs. 

9f  feet 
95.553 
5.308 
2.654 
103.515  pounds. 

EXAMPLE  4. — What  is  the  weight  of  a  BAR  OF  FLAT  IRON  £  of  an 
inch  in  thickness  by  5£  inches  in  breadth,  and  7  feet  6^  inches  in 
length? 

Opposite  to  5£,  and  to  £  in  thickness,  in  column  9th,  page  53,  is 
13.307  Ibs.,  which  is  the  weight  of  such  a  bar  for  a  length  of  one  foot. 
Hence  13.307 

7  feet 

93.149  pounds. 

Then,  to  determine  the  weight  for  6£  inches,  proceed  as  shown  above, 
in  example  2,  or  in  the  following  manner : 

Divide  the  weight  for  one  foot  by  12  (12  inches),  and  the  result 
is  the  weight  for  one  inch  in  length. 

Thus  ^=1-109. 

Then  1.109 

multiplied  by  6£ 

6.654 
554 

is  equal  to  7.208  pounds, 

which,  added  to  the  93.149  before  obtained,  is  equal  to  100.357 
pounds. 


56  CAST   AND   WROUGHT   IRON   AND   LEAD. 


CAST  IRON. 

To  ascertain  the  weight  of  a  cast  iron  BOLT  or  BAR,  find  the  weight 
of  a  wrought  iron  bolt  or  bar  of  the  same  dimensions  in  the  preced- 
ing tables,  and  from  the  weight  deduct  the  -j^-th  part ; 

Or,  as  486.65  :  450.55 : :  the  weight  in  the  table  :  to  the  weight  re- 
quired. 

EXAMPLE. — What  is  the  weight  of  a  piece  of  cast  iron  4  X  3f  X  12 
inches  ? 

In  table,  page  53,  the  weight  of  a  piece  of  wrought  iron  of  these 
dimensions  is  50.692  Ibs. 

Then  486.65  :  450.55::  50.692  :  46.93  Ibs. 


To  find  the  weight  of  a  piece  of  CAST  or  WROUGHT  IRON  of  any 
size  or  shape. 

Find  the  number  of  cubic  inches  in  the  piece,  multiply  them  by 
the  weight  of  a  cubic  inch,  and  the  product  will  be  the  weight  in 
pounds, 

EXAMPLE  1. — What  is  the  weight  of  a  block  of  WROUGHT  IRON 
10  inches  square  by  15  inches  in  length  ? 
10x10x15  =  1500  cubic  inches. 

.2816  weight  of  a  cubic  inch  of  wrought  iron. 
442.4000  pounds. 

EXAMPLE  2. — "What  is  the  weight  of  a  CAST  IRON  ball  15  inches 
in  diameter? 

By  table,  page  62,  a  cast  iron  ball  15  inches  in  diameter 
=  176.7149  cubic  inches. 

.2607  weight  of  a  cubic  inch  of  cast  iron. 
460.6957  pounds. 


LEAD. 

To  ascertain  the  weight  of  Lead. 

RULE. — Find  the  number  of  cubic  inches  in  the  piece,  multiply 
them  by  .41015,  and  the  product  will  be  the  weight  in  pounds. 

EXAMPLE. — What  is  the  weight  of  a  leaden  pipe  12  feet  long,  3| 
inches  in  diameter,  and  1  inch  thick  ? 
Area  of  (34  +  1  +  1)=  25.967 
"      "    3|  =  11.044 

Difference,  14.923,  or  area  of  ring. 

144  =12  feet. 

2148.912  X. 41015^881.376  pounds. 


WEIGHT   OF   COPPER   BOLTS   AND    COPPER. 


57 


WEIGHT  OF  COPPER  BOLTS  OR  RODS, 

From  i  to  4  inches  in  diameter. 

ONE  FOOT  IN  LENGTH. 


Diameter. 

Pounds. 

Diameter. 

Pounds. 

Diameter. 

Pounds. 

•1 

.1892 

I.f 

3.8312 

2-1 

17.0750 

•A 

.2956 

*'A 

4.2688 

24 

18.9161 

I 

.4256 

l.J 

4.7298 

24 

20.8562 

>& 

.5794 

i-A 

5.2140 

2-1 

22.8913 

.7567 

5.7298 

24 

25.0188 

.JL 

.9578 

i-A 

6.2547 

3. 

27.2435 

4 

1.1824 

14 

6.8109 

34 

29.5594 

•B 

1.4307 

i-A 

7.3898 

M 

31.9722 

4 

1.7027 

i.f 

7.9931 

3.| 

34.4815 

•H 

1.9982 

i.f 

9.2702 

3.J 

37.0808 

2.3176 

i-l 

10.6420 

34 

39.7774 

•ii 

2.6605 

2. 

12.1082 

34 

42.5680 

1. 

3.0270 

2-1 

13.6677 

3-1 

45.4550 

ii 

3.4170 

2-i 

15.3251 

4. 

48.4330 

To  find  the  weight  of  a  bolt  or  rod  of  a  greater  or  less  length  than 
one  foot,  proceed  as  by  the  rules  given  in  pages  54  and  55,  to  find 
the  weights  of  wrought  iron  bolts  or  bars. 


COPPER. 

To  ascertain  the  weight  of  copper. 

RULE. — Find  the  number  of  cubic  inches  in  the  piece,  multiply 
by  .32118,  and  the  product  will  be  the  weight  in  pounds. 

EXAMPLE. — What  is  the  weight  of  a  copper  plate  i  an  inch  thick 
by  16  inches  square  ? 

16X16=256 

.5  for  \  an  inch. 
128.0  X. 32118=41.111  pounds. 

BRAZIER'S  SHEETS  are  30  x  60  inches,  and  from  12  to  100  Ibs.  per 
square  foot. 

SHEATHING  COPPER  is  14  X  48  inches,  and  from  14  to  34  oz.  per 
square  foot. 

C2 


58      WEIGHT   OF  A  SQUARE   FOOT  OF  CAST   IKON,  ETC. 


WEIGHT  OF  A  SQUAEE  FOOT  OF  CAST  AND  WROUGHT 
IRON,  COPPER,  AND  LEAD, 


From 


to  2  inches  thick. 


Thickness. 

Cast  Iron. 

Wrought  Iron. 
Hard  rolled. 

Copper. 
Hard  rolled. 

Lead. 

Pounds. 

Pounds. 

Pounds. 

Pounds. 

•T5 

2.346 

2.517 

2.890 

3.691 

4 

4.693 

5.035 

5.781 

7.382 

•A 

7.039 

7.552 

8.672 

11.074 

.1 

9.386 

10.070 

11.562 

14.765 

.5^ 

11.733 

12.588 

14.453 

18.456 

4 

14.079 

15.106 

17".  344 

22.148 

A 

16.426 

17.623 

20.234 

25.839 

4 

18.773 

20.141 

23.125 

29.530 

•A 

21.119 

22.659 

26.016 

33.222 

4 

23.466 

25.176 

28.906 

36.913 

*H 

25.812 

27.694 

31.797 

40.604 

•I 

28.159 

30.211 

34.688 

44.296 

.ft 

30.505 

32.729 

37.578 

47.987 

4 

32.852 

35.247 

40.469 

51.678 

•H 

35.199 

37.764 

43.359 

55.370 

i. 

37.545 

40.282 

46.250 

59.061 

14 

42.238 

45.317 

52.031 

66.444 

i.j 

46.931 

50.352 

57.813 

73.826 

14 

51.625 

55.387 

63.594 

81.210 

14 

56.317 

60.422 

69.375 

88.592 

14 

61.011 

65.458 

75.156 

95.975 

i.| 

65.704 

70.493 

80.938 

103.358 

14 

70.397 

75.528 

86.719 

110.740 

2. 

75.090 

80.563 

92.500 

118.128 

WEIGHT   OF   RIVETED    COPPER   PIPES   AND   BRASS.       59 


WEIGHT  OF  RIVETED  COPPER  PIPES, 

From  5  to  31  inches  in  diameter,  and  from  fyhs  to  &ths  thick. 

ONE   FOOT   IN   LENGTH. 


Diameter 
in  inches. 

Thickness 
in  16ths. 

Weight  in 
pounds. 

Diameter 
in  inches. 

Thickness 
in  16ths. 

Weight  in 
pounds. 

5. 

3 

12.497 

15. 

5 

59.588 

5. 

4 

16.880 

16. 

4 

50.752 

k| 

3 

13.628 

16. 

5 

63.470 

5.| 

4 

18.395 

17. 

4 

53.856 

6. 

3 

14.765 

17. 

5 

67.344 

6. 

4 

19.908 

18. 

4 

57.037 

€.| 

3 

15.897 

18. 

5 

71.258 

64 

4 

21.415 

19. 

4 

60.142 

7. 

3 

17.034 

19. 

5 

75.233 

7. 

4 

22.932 

20. 

5 

78.208 

74 

4 

24.447 

21. 

5 

82.984 

8. 

4 

25.961 

22. 

5 

86.771 

84 

4 

27.471 

23. 

5 

90.571 

9. 

4 

28.985 

24. 

5 

94.308 

94 

4 

30.598 

25. 

5 

98.122 

10. 

4 

32.208 

26. 

5 

101.897 

11. 

4 

35.200 

27. 

5 

105.700 

12. 

4 

38.456 

28. 

5 

109.446 

13. 

4 

41.456 

29. 

5 

113.221 

14. 

4 

44.640 

30. 

5 

116.997 

15. 

4 

47.646 

31. 

5 

120.772 

The  above  weights  include  the  laps  on  the  sheets  for  riveting  and 
calking. 

The  weights  of  the  rivets  are  not  added ;  the  number  per  lineal 
foot  of  pipe  depends  upon  their  diameter,  and  their  size  upon  the 
thickness  of  the  metal  of  the  pipe. 


BRASS. 

To  ascertain  the  iceight  of  brass  castings. 

RULE. — Find  the  number  of  cubic  inches  in  the  piece,  multiply 
them  by  .3112,  and  the  product  will  be  the  weight  in  pounds. 


60 


WEIGHT   OF    CAST   IRON   PIPES. 


WEIGHT  OF  CAST  IKON  PIPES, 

OF   DIFFERENT   THICKNESS, 
From  1  inch  to  36  inches  bore. 

ONE   FOOT   IN   LENGTH. 


Bore. 

Th'kness. 

Weight. 

Bore. 

Th'kness. 

Weight. 

Bore. 

Th'kness. 

Weight, 

inches. 
1. 

inches. 
.1 

pounds. 

3.06 

inches. 

inches. 

pounds. 

25.70 

inches. 

9. 

inches. 
1. 

pounds. 

97.98 

i 

5.05 

"* 

"I 

32.91 

94 

48.98 

1^1 

3.67 

.f 

40.43 

_i 

62.02 

4 

1 

6. 

5. 

i 

26.94 

ts. 

75.32 

14 

6.89 

•K 

34.34 

•8 

88.98 

•i 

9.80 

.£ 

42.28 

1. 

102.90 

1  £ 

o 

7.80 

54 

4 

29.40 

10. 

4 

51.46 

•*••  4 

"f 

11.04 

•f 

37.44 

•t 

65.08 

•  2 

.s. 

45.94 

s. 

78.99 

2. 

'•1 

8.74 
12.23 

6. 

4 

31.82 
40.56 

1* 

93.24 
108.84 

2.J 

•f 

9.65 

"I 

49.60 

104 

1 

53.88 

4 

13.48 

*I 

58.96 

•1" 

68.14 

24 

:! 

10.57 
14.66 
19.05 

64 

:j 

34.32 
43.68 
53.30 

i! 

82.68 
97.44 
112.68 

2.f 

•f 

11.54 

*f 

63.18 

11. 

i 

56.34 

;| 

15.91 
20.59 

7. 

i 

36.66 
46.80 

j 

71.19 
86.40 

3. 

i 

12.28 

*i 

56.96 

•8 

101.83 

_i 

17.15 

*t 

67.60 

1. 

117.60 

•i" 

22.15 

i! 

78.39 

11.3- 

.£ 

58.82 

•i 

27.56 

74 

39.22 

1 

74.28 

3.J 

•j 

18.40 
23.72 

'1 

49.92 
60.48 

90.06 
106.14 

.f 

29.64 

•I 

71.76 

l'. 

122.62 

34 

•t 

19.66 
25.27 

i! 

83.28 
41  64 

12. 

i 

61.26 
77.36 

ri 

31.20 

. 

*f 

52  .'68 

«i 

93.70 

3.f 

20.90 

*• 

64.27 

•8 

110.48 

•f 

26.83 

*i 

76.12 

1- 

127.42 

mS. 

33.07 

j_ 

88.20 

124 

4 

63.70 

4. 

1 

22.05 
28.28 

84 

•f 

44.11 
56.16 

j 

80.40 
97.40 

4 

' 

:l 

34.94 
23.35 

:.l 

68. 
80.50 

l. 

114.72 
132.35 

•I 

29.85 

1. 

93.28 

13. 

.i 

66.14 

\£ 

36.73 

9. 

•. 

46.50 

•1 

83.46 

44 

: 

24.49 
31.40 
38.58 

I 

58.92 
71.70 
84.70 

i! 

101.08 
118.97 
187.28 

WEIGHT   OF   CAST  IRON   PIPES. 


61 


Bore.     Th'kness. 

Weight. 

Bore.  |  Th'kness. 

Weight. 

Bore. 

Th'kness. 

Weight. 

inches. 

134 

inches. 

pounds. 

68.64 
86.55 

inches. 

174 

inches. 

pounds. 

88.23 
111.06 

inches. 

27. 

inches. 

1 

pounds. 

204.04 
239.08 

ms. 

104.76 

•f 

134.16 

1. 

274.56 

| 

123.30 

•8 

157.59 

28. 

^ 

211.32 

l'. 

142.16 

1. 

181.33 

•1 

247.62 

14. 

•i 

71.07 

18. 

A 

114.10 

1. 

284.28 

i 

89.61 

.4 

137.84 

29. 

s 

218.70 

SL 

108.46 

•\ 

161.90 

'? 

256.20 

•t 

127.60 

1. 

186.24 

i! 

294.02 

i. 

147.03 

19. 

•I 

120.24 

30. 

226.20 

144 

4 

73.72 

.3. 

145.20 

"i 

264.79 

•1 

92.66 

•8 

170.47 

1 

303.86 

•f 

112.10 

1. 

195.92 

l"i 

343.20 

i!8 

131.86 
151.92 

20. 

i 

126.33 
152.53 

31. 

:| 

233.40 
273.40 

15. 

4 

75.96 

.1 

179.02 

8 

313.68 

I 

95.72 

i. 

205.80 

14 

354.24 

i; 

115.78 
136.15 
156.82 

21. 

i 

132.50 
159.84 
187.60 

32. 

,? 

240.76 
281.94 
323.49 

154 

•1 

78.40 

i*. 

215.52 

1.1 

365.29 

i 
i! 

98.78 
119.48 
140.40 
161.82 

22. 

i. 

138.60 
167.24 
196.46 
225.38 

33. 

8 

l.'8 
1.1 

248.10 
290.50 
333.24 
376.26 

16. 

J 

80.87 
101.82 
123.14 
144.76 
166.60 

23. 

i.*8 

144.77 
174.62 
204.78 
235.28 

34. 

8 

255.45 
298.88 
342.88 
387.13 

J-  • 

24. 

* 

150.85 

}B£ 

431.76 

164 

I 

83.30 
104.82 
126.79 

140  no 

i! 

181.92 
213.28 
245.08 

35. 

;i 

262.70 
307.62 
352.86 

i! 

X6b«7,  \}£i 

171.60 

25. 

i 

156.97 
189.28 

1:| 

398.10 
443.96 

17. 

i. 

85.73 
107.96 
130.48 
153.30 
176.58 

26. 

i! 

i. 

221.94 
254.86 
196.62 
230.56 
264.66 

36. 

1:1 

270.18 
316.36 
362.86 
409.34 
456.46 

62        WEIGHT,  ETC.,  OF  CAST  IKON   AND  LEAD  BALLS. 


WEIGHT  AND  CAPACITY  OF  CAST  IKON  AND  LEAD 
BALLS, 

From  1  to  20  inches  in  diameter. 


Diameter  in 
inches. 

Capacity  in  cubic 
inches. 

CAST  IRON. 

Weight  in  pounds. 

LEAD. 

Weight  in  pounds. 

1. 

.5236 

.1365 

.2147 

1.1 

1.0227 

.2666 

.4195 

1-1 

1.7672 

.4607 

.7248 

1.1 

2.8062 

.7316 

1.1510 

2. 

4.1888 

1.0920 

1.7180 

2.1 

5.9641 

1.5548 

2.4462 

2.1 

8.1812 

2.1328 

3.3555 

*         2.1 

10.8892 

2.8388 

4.4662 

3. 

14.1372 

3.6856 

5.7984 

3.1 

17.9742 

4.6859 

7.3721 

3.1 

22.4493 

5.8525 

9.2076 

3.f 

27.6117 

7.1984 

11.3249 

4. 

33.5104 

8.7362 

13.7443 

4.1 

40.1945 

10.4787 

16.4858 

4.£ 

47.7130 

12.4388 

19.5695 

4.1 

56.1152 

14.6292 

23.0156 

6. 

65.4500 

17.0628 

26.8443 

5.1 

75.7675 

19.7523 

31.0756 

5.f 

87.1139 

22.7106 

35.7298 

6.1 

99.5413 

25.9504 

40.8269 

6. 

113.0976 

29.4845 

46.3870 

6.1 

127.7020 

33.2919 

52.3770 

6.} 

143.7937 

37.4870 

58.9768 

6.| 

161.0315 

41.9809 

66.0471 

7. 

179.5948 

46.8204 

73.6608 

7.1 

199.5325 

52.0188 

81.8382 

7.1 

220.8937 

57.5870 

90.5995 

7.1 

243.7276 

63.5397 

99.9649 

8. 

268.0832 

69.8893 

109.9543 

8.1 

294.0096 

76.6483 

120.5880 

8.1 

321.5558 

83.8296 

131.8861 

8.1 

350.7711 

91.4460 

143.8688 

9. 

381.7044 

99.5103 

156.5560 

9.£ 

448.9215 

117.0338 

184.1251 

10. 

523.6000 

136.5025 

214.7545 

11. 

696.9116 

181.6849 

285.8383 

12. 

904.7808 

235.8764 

371.0959 

13. 

1150.349 

299.8960 

471.8158 

14. 

1436.7584 

374.5629 

589.2865 

15. 

1767.1500 

460.6960 

724.7966 

16. 

2144.6657 

559.1143 

879.6346 

17. 

2572.4468 

670.6368 

1055.0891 

18. 

3053.6352 

796.0827 

1252.4486 

19. 

3591.3724 

936.2708 

1473.0014 

20. 

4188.8000 

1092.0202 

1718.0363 

NOTE. — If  the  weight  in  Wrought  Iron  or  Copper  is  required,  mul- 
tiply the  capacity  of  the  ball  by  .2816  for  the  former,  and  .32118 
for  the  latter. 


WEIGHT   OP  LEAD    PIPE. 


63 


WEIGHT  OF  LEAD  PIPE  PER  YARD, 

From  f  to  5  inches  diameter. 

WATER   PIPES   FOR   HYDRANTS,   PUMPS,  ETC. 


Diameter 
of  bore  in 
inches. 

Thickness  in 
l-100ths  of  an 
inch. 

Weight  per 
foot  in 
pounds. 

Diameter 
of  bore  in 

Thickness  in 
1-lOOths  of  an 
inch. 

Weight  per 
foot  in 
pounds. 

•t 

6 

.424 

14 

14 

3.5 

8 

.625 

17 

4.25 

12 

1. 

19 

5. 

16 

1.25 

23 

6.5 

19 

1.5 

27 

8. 

•i 

7 

.545 

l.f 

13 

4. 

9 

.75 

17 

5. 

11 

1. 

21 

6.5 

13 

1.25 

27 

8.5 

16 

1.75 

2. 

15 

4.75 

19 

2. 

18 

6. 

* 

8 

.727 

22 

7. 

9 

1. 

27 

9. 

13 
16 

1.5 
2. 

24 

&  of  an  in. 

8. 
11. 

20- 

2.5 

f« 

14. 

22 

3. 

<« 

17. 

•1 

8 

.969 

3. 

3            (( 

9. 

10 

1.25 

*F    " 

12. 

12 

1.75 

!>           it 

16. 

16 

2.25 

^          " 

20*. 

20 

3 

23 

3.'5 

34 

3T        " 

12.5 

15. 

1. 

10 

1.5 

JL    << 

18.5 

11 

2 

^    " 

22. 

14 
17 
21 
24 

2.'5 
3.25 
4. 
4.75 

4. 

!  I 

12. 
16. 
21. 

25. 

i.i 

10 
12 
14 

2. 
2.5 
3. 

44 

8 
f          r' 

14. 
18. 

16 

3.75 

5. 

t            " 

20. 

19 

4.75 

1            " 

31. 

25 

6. 

WASTE  PIPE. 


H  inch  diam.  2  Ibs.  per  foot. 

2  "          3  Ibs.         « 

3  "          3£  and  5  Ibs. 
foot. 


per 


4  in.  diam.  5,  6,  and  8  Ibs.  per  ft. 
4|fV  .  ."       6  and  8  Ibs.        " 

5  "       8,  10,  and  12  Ibs.  per 
foot. 


64        WEIGHT,  ETC.,  OF  METALS  BY  THE  WIRE  GUAGE. 


WEIGHT  OF  A  SQUARE  FOOT  OF  WROUGHT  IRON, 

AS    PER    BIRMINGHAM    WIRE    GUAGE, 


No.  of 
Guage. 

Lbs. 

No.  of 
Guage. 

Lbs. 

No.  of 
Guage. 

Lbs. 

No.  of 
Guage. 

Lbs. 

1 

2 

3 

4 
5 
6 

7 

12.55 
11.25 
10.45 
9.55 
8.66 
8.34 
7.5 

8 
9 
10 
11 

12 
13 
14 

6.64 
6.29 
5.5 
4.73 
4.3 
3.64 
3.23 

15 
16 
17 
18 
19 
20 

2.97 
2.62 
2.19 
1.92 
1.7 
1.41 

21 
22 
23 

24 
25 
26. 

1.32 
1.15 
.99 
.95 
.84 
.78 

VALUES  OF  THE  BIRMINGHAM  GUAGES, 
For  Iron  Wire  and  for  Sheet  Iron  and  Steel. 


No. 

Inches. 

No. 

Inches. 

No.     !      Inches. 

No. 

Inches. 

0 

.340 

10 

.134 

19 

.042 

28 

.014 

1 

.300 

11 

.120 

20 

.035 

29 

.013 

2 

.284 

12 

.109 

21 

.032 

30 

.012 

3 

.259 

13 

.095 

22 

.028 

31 

.010 

4 

.238 

14 

.083 

23 

.025 

32 

.009 

5 

.220 

15 

.072 

24 

.022 

33 

.008 

6 

.203 

16 

.065 

25 

.020 

34 

.007 

7 

.180 

17 

.058 

26 

.018 

35 

.005 

8 

.165 

18 

.049 

27 

.016 

36 

.004 

S  9 

.148 

For  Sheet  Brass,  Silver,  Gold,  frc. 

1 

.004 

10 

.024 

19 

.064 

28 

.120 

2 

.005 

11 

.029 

20 

.067 

29 

.124 

3 

.008 

12 

.034 

21 

.072 

30 

.126 

4 

.010 

13 

.036 

22 

.074 

31 

.133 

5 

.012 

14 

.041 

23 

.077 

32 

.143 

6 

.013 

15 

.047 

24 

.082 

33 

.145 

7 

.015 

16 

.051 

25 

.095 

34 

.148 

8 

.016 

17 

.057 

26 

.103 

35 

.158 

9 

.019 

18 

.061 

27 

.113 

36 

.167 

MISCELLANEOUS. 


G5 


LAP-WELDED  IRON  BOILER  TUBES  (Prosser's  Patent). 
TABLE  of  the  Diameter,  Thiclcness,  and  Weight  of  Iron  Boiler  Tubes. 


External 
Diameter. 

Wire  Guage. 

Weight. 

per  foot. 

Diameter. 

Thickness  of 
Wire  Guage. 

Average 
Weight. 

Price 
per  foot. 

Inches. 

No. 

Ibs.  per  ft. 

Cents. 

Inches. 

No. 

Ibs.  per  ft. 

*     c. 

If 

16 

1 

20 

2| 

12i 

21- 

48 

11 

15 

ij 

29 

3 

" 

3^7 

51 

If 

13 

if 

31 

8* 

12 

4 

85 

2 

" 

2 

34 

4 

11 

5 

1  10 

2 

" 

2 

" 

5 

10 

6| 

1  50 

2f 

M 

2| 

39 

6 

" 

9 

2  20 

9 

12| 

2-i9o 

43 

7 

8 

12 

3  00 

2ft 

14 

21 

46 

8 

7 

16 

4  00 

SCREWS. 

TABLE  showing  the  Number  of  Threads  to  an  Inch  in  V  thread 
Screws. 


Diam.  in  inches,  £  -^ 

No.  of  threads,'  20  18 

Diam.  in  inches,  If  If 

No.  of  threads,  6  5 

Diam.  in  inches,  3|  4 

No.  of  threads,  3  3 


16  14  12  11  10  9  8   7 

1|  If  2  2i  2J  2f   3 
5  44  44  4   4   34  34 

4£  44   4|   5  5£  54 
2£  2$   2|  2f  2f  2$ 


1*    If 

76 

3i     34- 
3i     3^ 

5|      6 


The  depth  of  the  threads  should  be  half  their  pitch. 

The  diameter  of  a  screw,  to  work  in  the  teeth  of  a  wheel,  should 
be  such  that  the  angle  of  the  threads  does  not  exceed  10°. 


TIN. 


Description. 

Size  of  sheet. 

Mean  thickness. 

Mean  weight 
of  one  sheet. 

No  on  wire 
guage. 

Thickness  of  sheet. 

Single  ... 
Double  X 

inches. 

10x14 
10  xH 

31 
27 

inches. 
.0125  (or  80  to  1  inch) 
.0181  (or  55  to  1  inch) 

Ibs. 

0.5 
0.75 

There  are  usually  225  sheets  in  a  box. 


66  MISCELLANEOUS. 


ALLOYS  OF  COPPER  AND  TIN. 

GUN  METAL. 

Tin  to  be  added  to  1  pound  of  Copper. 


Soft  gun  metal 

Mathematical  instruments 

Wheels 

Guns,  large. 


small 


oz. 


.25 
.5 
.75 
.50 


Machinery  bearings 2  to  2.50 

Musical  bells 3 

Gongs,  cymbals,  &c 3.50 

House  bells,  small 4 

"        "       large 4.50 

Church  bells 5 

Speculum  metal 7  to  8 

Temper  metal  for  adding  small  quantities  of  copper,   32  oz. 


COPPER   AND   ZINC. 

Tin  to  be  added  to  I  pound. 

Copper  castings 1.125  to  1.50  oz 

Gilding  metal 1  "  1.50 

Tombac  (red  brass) 2 

Ked  sheet  brass.     Pinchbeck  and  Bath  metal 3  to  4 

Bristol  brass 6 

Ordinary  brass 8 

Muntz's  metal  for  ship  fastenings,  sheathing,  &c..  10.66 

Soft  spelter  solder 16 


COPPEE,  ZINC,  TIN,  AND   LEAD. 

Tin.  Zinc.  Copper.          Brass. 

Extremely  tenacious 1.5  oz.    .5  oz.  16  oz. 

Wheels 1.5"  16"      2     oz. 

For  turning 2      "  1.5  " 

Bearings,  Nuts,  &c 2.5  "  1.5  " 


MISCELLANEOUS.  67 


SOLDERS. 

For  Lead,  melt  1  part  of  Block  Tin,  and  when  in  a  state  of  fusion, 
add  2  parts  of  Lead.     Resin  should  be  used  with  this  solder. 

For  Tin,  Pewter  4  parts,  Tin  1,  and  Bismuth  1 ;  melt  them  to- 
gether.    Resin  is  also  used  with  this  solder. 

For  Iron,  tough  Brass,  with  a  small  quantity  of  Borax. 


CEMENTS. 
Glue.     Powdered  chalk  added  to  common  glue  strengthens  it. 

A  glue  which  will  resist  the  action  of  water  is  made  by  boiling  1 
pound  of  glue  in  2  quarts  of  skimmed  milk. 

Soft  Cement.     For  steam-boilers,  steam-pipes,  &c.     Red  or  white 
lead  in  oil,  4  parts ;  iron  borings,  2  to  3  parts. 

Hard  Cement.     Iron  borings  and  salt  water,  and  a  small  quantity 
of  sal  ammoniac  with  fresh  water. 

Cement,  Ashes,  2  parts}  mixed  ^  oil   ^  regist  ^  weather 
Sand,    1     «    )      equal  to  marble. 

HYDRAULIC    CEMENT. 

A  barrel  contains  300  Ibs.,  equal  to  four  struck  bushels. 

BROWN  MORTAR. 

One  third  Thomaston  lime, 

Two  thirds  sand,  and  a  small  quantity  of  hair. 

Lime  and  sand,  and  cement  and  sand,  lessen  about  £  in  bulk 
when  made  into  mortar. 

DIGGING. 

23  cubic  feet  of  sand,  or  18  cubic  feet  of  earth,  or  17  cubic  feet 
of  clay,  make  a  ton. 

18  cubic  feet  of  gravel  or  earth  before  digging,  make  27  cubic 
feet  when  dug. 


68 


MISCELLANEOUS. 


GAS  PIPES. 

TABLE  of  the  Diameter  and  Length  of  Gas  Pipes  to  transmit  given 
.  Quantities  of  Gas  to  branch  Pipes  and  Burners. — Dr.  URE. 


No.  of  cubic  feet  of  gas  per  hour. 

Length  of  pipe  in  feet. 

Diameter  of  pipe  in  inches. 

50 

100 

0.40 

250 

200 

1. 

500 

600 

1.97 

700 

1000 

2.65 

1000 

1000 

3.16 

1500 

1000 

3.87 

2000 

1000 

4.47 

2000 

2000, 

5.32 

2000 

4000 

6.33 

2000 

6000 

7. 

6000 

1000 

7.75 

6000 

2000 

9.21 

8000 

1000 

8.95 

8000 

2000 

16.65 

These  dimensions  are  applicable  to  the  mains  which  conduct  the 
gas  to  the  places  where  it  is  to  be  used.  If  they  send  oft'  branches 
for  burners,  the  diameter  may  be  reduced,  or  the  length  may  be 
greater. 

For  example,  if  a  pipe  of  5.32  inches,  which  transmits  2000  cubic 
feet  through  a  length  of  2000  feet,  gives  off,  in  this  space,  1000  cubic 
feet  of  gas,  then  the  same  diameter  can  continue  to  transmit  the 
gas  through  a  length  of  2450  feet. 


CISTERNS. 

CAPACITY   OF  CISTERNS    IN   U.  S.  GALLONS, 

For  each  10  inches  in  depth. 


2* 
3 


5 

5i 

6 

6* 

7 
1\ 


19.5 

8    feet  di 

8*        •  1, 
9 

10 
11 
12 
13 
14 
15 
20           -   « 

ameter  

313.33 
353.72 
396.56 
461.40 
489.20 
592.40 
705. 
827.4 
959.6 
1101.6 
1958.4 
5>,or>«  9 

30  6 

44  06 

5997 

78  33 

99.14 

122.40 
148  10 

17625 

206  85 

239.88 

..   275.40 

MISCELLANEOUS. 


69 


WEIGHTS  OF  VARIOUS  SUBSTANCES. 


Cubic  foot  in  pounds. 

Cubic  inch  in  pounds. 

1378.94 

.798 

Gold                               

1204.41 

.697 

850.18 

.492 

Lead.                              

708.75 

.41015 

Silver   

654.91 

.379 

Copper                             .... 

555 

.32118 

Brass     

537.75 

.3112 

Steel 

489  8 

.2834 

"Wrought  Iron  

486.65 

.2816 

Tin 

456 

.263 

Cast  Iron    

450.55 

.2607 

Zinc 

428  54 

.248 

Granite  

164.16 

.095 

Clay... 

135. 

.0756 

Stron01  soil 

127. 

.0735 

Brick  

125. 

.0723 

Common  soil  

124. 

.0717 

Coal  (anthracite) 

9504 

.055 

"     (bituminous)  

81.22 

.047 

Loose  earth  or  sand  
Live  Oak            

95. 
70. 

.0549 
.040 

Hickory  

51.84 

.030 

White  Oak             

45.2 

.026 

44.93 

.026 

Salt  Water  (sea)  

64.3 

.03721 

Fresh  Water 

62  5 

.03616 

Yellow  Pine    

33.81 

.019 

White  Pine  

29.56 

.0171 

Tallow                   

59. 

.03414 

Cork   

15. 

.00868 

Air 

.07529 

Steam  

.03689 

— 

WEIGHT  OF  COMPOSITION  SHEATHING  NAILS. 


Number.     |      L^ta 

Number  in  a 
pound. 

Number.       |       **£$£* 

Number  in  a 
pound. 

1 

I 

290 

8 

1| 

168 

2 

1 

260 

9 

*J 

110 

3 

1 

212 

10 

If 

101 

4 

4 

201 

11 

If 

74 

5 

H 

199 

12 

2 

64 

6 

i 

190 

13 

i| 

59 

7    . 

a 

184 

70 


MISCELLANEOUS. 


SLATING. 

Sizes  of  Slates. 

Doubles 14  by  6  inches. 

Ladies' 15  *'  8 

Countess 22  '  11 

Duchess 26  '  15 

Imperial  and  Patent 32  '  26 

and  Queens 39  '  27 


HEMPEN  CORDS. 

Hempen  Cords,  when  twisted,  will  support  the  following  weights 
to  the  square  inch  of  their  section. 


U>s. 

i  to  1  inch  diameter 8.746 

1  to  3  inches  diameter  ....  6.800 


Lba. 

3  to  5  inches  diameter  ....  5.345 
5  to  7  inches  diameter  ....  4.860 


STRENGTH  AND  STIFFNESS  OF  METALS, 

Cast  Iron  being  1. 

Strength.  Stiffness. 

Wrought  Iron 1.12  1.3 

Brass 435  .49 

Zinc 365  .76 

Tin 182  .25 

Lead 046  .0385 


PAINTS  AND  LACKERS. 
White  Paint. 

Inside  work. 

White-lead,  ground  in  oil 80. 

Boiled  oil 14.5 

Raw  oil — 

Spirits  turpentine 8. 


Outside  work. 

80 
9 
9 
4 


New  wood  work  requires  about  1  Ib.  to  the  square  yard  for  3  coats. 


Lead  Color. 


White-lead,  ground  in  oil.  75 

Lampblack 1 

Boiled  linseed  oil 23 


Litharge 5 

Japan  varnish 5 

Spirits  turpentine 2.5 


The  turpentine  and  varnish  are  added  as  the  paint  is  required  for 
use  or  transportation. 

Gray  or  Stone  Color. 


White-lead,  in  oil 78. 

Boiled  oil . 9.5 

Raw  oil 9.5 


Spirits  turpentine 3. 

Turkey  umber 5 

Lampblack 25 


1  square  yard  of  new  brick  work  requires,  for  2  coats,  1.1  Ib. ;  for 
3  coats,  1.5  Ib. 

Cream  Color. 

1st  coat.  3d  coat. 

White-lead,  in  oil 66.6  70. 

French  yellow 3.3  3.3 

Japan  varnish 1.3  1.3 

Raw  oil 28.  24.5 

Spirits  turpentine 2.25'  2.25 

1  square  yard  of  new  brick  work  requires,  for  1st  coat,  0.75  ;  for 
2d  coat,  0.3  Ib. 

Black  Paint  (for  Iron). 


Lampblack 28 


Litharge 1 

Japan  varnish 1 

The  varnish  and  turpentine  are  added  last. 

Liquid  Olive  Color. 


Linseed  oil,  boiled 73 

Spirits  turpentine 1 


Olive  paste 61.5 

Boiled  oil...  ..  29.5 


Spirits  turpentine 5.5 

Paint  for  Tarpaulins  (Olive). 


Dryings 3.5 

Japan  varnish 2. 


Liquid  olive  color 1 00 


Spirits  turpentine 6 


Beeswax 6 

1  square  yard  requires  2  Ibs.  for  3  coats. 

Dissolve  the  beeswax  in  the  turpentine,  and  mix  the  paint  warm. 

LACKER%/br  Iron  Ordnance. 


Black-lead,  pulverized 12 

Litharge 5 

Linseed  oil....  ..  66 


Red-lead 11 

Lampblack  5 


Boil  it  gently  for  about  20  minutes,  stirring  it  constantly  during 
that  time. 


72 


Lacker  for  Small  Arms,  or  for  Water  Proof  Paper. 


Beeswax  .....................  18.     I  Spirits  turpentine  ...........  80 

Boiled  linseed  oil  .........     3.5  I 

Heat  the  ingredients  in  a  copper  or  earthen  vessel  over  a  gentle 
fire,  in  a  water  bath,  until  they  are  well  mixed. 

Lacker  for  Bright  Iron  Work. 

Linseed  oil,  boiled  ........  80.5     I  Litharge  .....................  5.5 

White-lead,  ground  in  oil  11.25  |  Pulverized  resin  ...........  2.75 

Add  the  litharge  to  the  oil  ;  let  it  simmer  over  a  slow  fire  for  3 
hours  ;  strain  it,  and  add  the  resin  and  white-lead  ;  keep  it  gently 
warmed,  and  stir  it  until  the  resin  is  dissolved. 


STAINING  WOOD  AND  IVORY. 

Yellow.    Dilute  nitric  acid  will  produce  it  on  wood. 

Red.  An  infusion  of  Brazil-wood  in  stale  urine,  in  the  propor- 
tion of  a  Ib.  to  a  gallon  for  wood,  to  be  laid  on  when  boiling  hot, 
and  should  be  laid  over  with  alum  water  before  it  dries. 

Or,  a  solution  of  dragon's  blood  in  spirits  of  wine  may  be  used. 

Black.     Strong  solution  of  nitric  acid,  for  wood  or  ivory. 

Mahogany.  Brazil,  Madder,  and  Logwood,  dissolved  in  water  and 
put  on  hot. 

Blue.  Ivory  may  be  stained  thus  :  Soak  it  in  a  solution  of  verdi- 
gris in  nitric  acid,  which  will  turn  it  green  ;  then  dip  it  into  a  solu- 
tion of  pearlash  boiling  hot. 

Purple.  Soak  ivory  in  a  solution  of  sal  ammoniac  in  four  times 
its  weight  of  nitrous  acid. 


THE    END. 


MARINE  GLUE. — In  response  to  J.  H.  P.'s  request  in  regard 

to  marine  glue,  (in  the  issue  of  22d  inst.),  I  must  refer  him  for  a  more  accu- 
rate formula  for  preparing  it  to  Tomlinson's  Encyclopaedia,  of  the  Arts  and 
Sciences,  article  on  glue  and  shellac.  I  have  not  the  book  at  hand,  and  it  is 
years  since  I  have  seen  it,  but  I  have  made  marine  glue  by  its  formula.  The 
ether  used  must  be  perfectly  free  from  alcohol,  as  that  fluid  acts  as  a  pre- 
cipitant upon  India  rubber.  Heat,  however,  must  be  applied  in  hastening 
a  solution ,  the  best  means  for  so  doing  being  the  sand  bath.  [In  my  arti- 
cle on  glues,  yon  made  me  say  "  take  the  scales  "  of  certain  fish ;  I  wrote, 
"  take  the  skins. "]— F.  L.  J. ,  of  Ark.  • 


A  CEMENT  OF  GKEAT  ADHESIVE  QUALITY,  particularly  said 
to  be  serviceable  in  attaching  the  brass  mountings  on  glass 
lamps,  as  it  is  unaffected  by  petroleum,  may  be  prepared  by 
boiling  three  parts  of  rosin  with  one  part  of  caustic  soda, 
and  five  parts  of  water,  thus  making  a  kind  of  soap,  which 
is  mixed  with  one-half  its  weight  of  plaster  of  Paris.  Zinc- 
white,  white  lead,  or  precipitated  chalk  may  be  used  instead 
of  the  plaster,  but  when  they  are  used  the  cement  will  be 


Q.  D.  O. — Glue  will  unite  leather,  and  becomes  very  strong 
if  mixed  with  white-lead  paint ;  such  a  mixture  was  sold  some 
time  ago  iu  the  streets  of  New- York  as  a  new  and  wonderful 
cement  for  uniting  leather  straps  and  belting  without  rivets. 
As  a  proof  of  its  strength,  a  heavily-loaded  two-horse  wagon 
was  drawn  by  leather  traces  made  of  pieces  of  leather,  all 
stuck  together  by  this  compound. 

A.  E.  S.,  of  Mo. — In  the  oxychloride  of  zinc  paint,  the  propor- 
tion of  oxide  of  zinc  used  may  be  varied.  It  should,  however,  not  be  less 
than  half  the  weight  of  the  chloride.  The  object  of  the  tartrate  of  potassa 
is  to  prevent  too  rapid  drying.  This  may,  therefore,  be  used  in  variable 
proportions.  The  amount  of  water  and  starch  used  depends  upon  the 
consistency  required.  Experience  can  be  the  only  sure  guide  in  these 
particulars.  By  a  few  preliminary  experiments  with  small  quantities 
you  will  probably  be  able  to  succeed. 


V 


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